{"id":68138,"date":"2021-08-30T16:04:00","date_gmt":"2021-08-30T10:34:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=68138"},"modified":"2023-12-01T10:35:30","modified_gmt":"2023-12-01T05:05:30","slug":"rd-sharma-solutions-class-11-maths-chapter-33-exercise-33-3","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-33-exercise-33-3\/","title":{"rendered":"RD Sharma Class 11 Solutions Chapter 33 Probability Exercise 33.3 (Updated for 2024)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-121470\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-33-Exercise-33.3.jpg\" alt=\"RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-33-Exercise-33.3.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-33-Exercise-33.3-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3:&nbsp;<\/strong>It is based on a set of axioms. Experts&#8217; key objective is to provide <a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-11-maths-rd-sharma-solutions\/\"><strong>RD Sharma Class 11 Solutions<\/strong><\/a> and thereby assist students, regardless of their intelligence level. To assist them in performing well on the board exams, the solutions are described and solved in easy to understand manner. Students can get <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-33-probability\/\"><strong>RD Sharma Solutions Class 11 Maths Chapter 33<\/strong><\/a> Exercise 33.3&nbsp;from the links provided below and save them for future use.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69e147f7a11ca\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 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href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-33-exercise-33-3\/#download-rd-sharma-class-11-solutions-chapter-33-probability-exercise-333-free-pdf\" title=\"Download RD Sharma Class 11 Solutions Chapter 33 Probability Exercise 33.3 Free PDF\">Download RD Sharma Class 11 Solutions Chapter 33 Probability Exercise 33.3 Free PDF<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-33-exercise-33-3\/#access-rd-sharma-solutions-class-11-maths-chapter-33-exercise-333-important-question-with-answers\" title=\"Access RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3- Important Question with Answers\">Access RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3- Important Question with Answers<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link 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href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-33-exercise-33-3\/#what-are-the-advantages-of-using-rd-sharma-solutions-class-11-maths-chapter-33-exercise-333\" title=\"What are the advantages of using RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3?\">What are the advantages of using RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-33-exercise-33-3\/#where-can-i-download-rd-sharma-solutions-class-11-maths-chapter-33-exercise-333-free-pdf\" title=\"Where can I download RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3 free PDF?\">Where can I download RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3 free PDF?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-class-11-solutions-chapter-33-probability-exercise-333-free-pdf\"><\/span>Download RD Sharma Class 11 Solutions Chapter 33 Probability Exercise 33.3 Free PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-11-Maths-Chapter-33-Ex-33.3-1.pdf\">RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3<\/a><\/p>\n<div id=\"example1\" style=\"text-align: justify;\">&nbsp;<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 800px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-11-Maths-Chapter-33-Ex-33.3-1.pdf\", \"#example1\");<\/script><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-rd-sharma-solutions-class-11-maths-chapter-33-exercise-333-important-question-with-answers\"><\/span>Access RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3- Important Question with Answers<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>1.<\/strong>&nbsp;<strong>Which of the following cannot be a valid assignment of probability for elementary events or outcomes of sample space S = {w<sub>1<\/sub>, w<sub>2<\/sub>, w<sub>3<\/sub>, w<sub>4<\/sub>, w<sub>5<\/sub>, w<sub>6<\/sub>, w<sub>7<\/sub>}:<br><img class=\"alignnone size-full wp-image-121514\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/kop1.png\" alt=\"1\" width=\"512\" height=\"539\"><br><\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>For each event to be a valid assignment of probability.<\/p>\n<p>The probability of each event in sample space should be less than 1 and the sum of probability of all the events should be exactly equal to 1.<\/p>\n<p><strong>(i)<\/strong>&nbsp;It is valid as each P (w<sub>i<\/sub>) (for i=1 to 7) lies between 0 to 1 and sum of P (w<sub>1<\/sub>) =1<\/p>\n<p><strong>(ii)<\/strong>&nbsp;It is valid as each P (w<sub>i<\/sub>) (for i=1 to 7) lies between 0 to 1 and sum of P (w<sub>1<\/sub>) =1<\/p>\n<p><strong>(iii)<\/strong> It is not valid as a sum of P (w<sub>i<\/sub>) = 2.8 which is greater than 1<\/p>\n<p><strong>(iv)<\/strong>&nbsp;it is not valid as P (w<sub>7<\/sub>) = 15\/14&nbsp;which is greater than 1<\/p>\n<p><strong>2. A die is thrown. Find the probability of getting:<br>(i) a prime number<br>(ii) 2 or 4<br>(iii) a multiple of 2 or 3<\/strong><\/p>\n<p><strong>Solution<\/strong>:<\/p>\n<p>Given: A die is thrown.<\/p>\n<p>The total number of outcomes is six, n (S) = 6<\/p>\n<p>By using the formula,<\/p>\n<p>P (E) = favourable outcomes \/ total possible outcomes<\/p>\n<p><strong>(i)<\/strong>&nbsp;Let E be the event of getting a prime number<\/p>\n<p>E = {2, 3, 5}<\/p>\n<p>n (E) = 3<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 3 \/ 6<\/p>\n<p>= \u00bd<\/p>\n<p><strong>(ii)<\/strong>&nbsp;Let E be the event of getting 2 or 4<\/p>\n<p>E = {2, 4}<\/p>\n<p>n (E) = 2<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 2 \/ 6<\/p>\n<p>= 1\/3<\/p>\n<p><strong>(iii)<\/strong>&nbsp;Let E be the event of getting a multiple of 2 or 3<\/p>\n<p>E = {2, 3, 4, 6}<\/p>\n<p>n (E) = 4<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 4 \/ 6<\/p>\n<p>= 2\/3<\/p>\n<p><strong>3.<\/strong>&nbsp;<strong>In a simultaneous throw of a pair of dice, find the probability of getting:<br>(i) 8 as the sum<br>(ii) a doublet<br>(iii) a doublet of prime numbers<br>(iv) an even number on first<br>(v) a sum greater than 9<br>(vi) an even number on first<br>(vii) an even number on one and a multiple of 3 on the other<br>(viii) neither 9 nor 11 as the sum of the numbers on the faces<br>(ix) a sum less than 6<br>(x) a sum less than 7<br>(xi) a sum more than 7<br>(xii) neither a doublet nor a total of 10<br>(xiii) odd number on the first and 6 on the second<br>(xiv) a number greater than 4 on each die<br>(xv) a total of 9 or 11<br>(xvi) a total greater than 8<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given: a pair of dice has been thrown, so the number of elementary events in sample space is 6<sup>2&nbsp;<\/sup>= 36<\/p>\n<p>n (S) = 36<\/p>\n<p>By using the formula,<\/p>\n<p>P (E) = favourable outcomes \/ total possible outcomes<\/p>\n<p><strong>(i)<\/strong>&nbsp;Let E be the event that the sum 8 appears<\/p>\n<p>E = {(2, 6) (3, 5) (4, 4) (5, 3) (6, 2)}<\/p>\n<p>n (E) = 5<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 5 \/ 36<\/p>\n<p><strong>(ii)<\/strong>&nbsp;Let E be the event of getting a doublet<\/p>\n<p>E = {(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)}<\/p>\n<p>n (E) = 6<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 6 \/ 36<\/p>\n<p>= 1\/6<\/p>\n<p><strong>(iii)<\/strong>&nbsp;Let E be the event of getting a doublet of prime numbers<\/p>\n<p>E = {((2, 2) (3, 3) (5, 5)}<\/p>\n<p>n (E) = 3<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 3 \/ 36<\/p>\n<p>= 1\/12<\/p>\n<p><strong>(iv)<\/strong>&nbsp;Let E be the event of getting a doublet of odd numbers<\/p>\n<p>E = {(1, 1) (3, 3) (5, 5)}<\/p>\n<p>n (E) = 3<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 3 \/ 36<\/p>\n<p>= 1\/12<\/p>\n<p><strong>(v)<\/strong>&nbsp;Let E be the event of getting sum greater than 9<\/p>\n<p>E = {(4,6) (5,5) (5,6) (6,4) (6,5) (6,6)}<\/p>\n<p>n (E) = 6<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 6 \/ 36<\/p>\n<p>= 1\/6<\/p>\n<p><strong>(vi)<\/strong>&nbsp;Let E be the event of getting even on first die<\/p>\n<p>E = {(2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)}<\/p>\n<p>n (E) = 18<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 18 \/ 36<\/p>\n<p>= \u00bd<\/p>\n<p><strong>(vii)<\/strong>&nbsp;Let E be the event of getting even on one and multiple of three on other<\/p>\n<p>E = {(2,3) (2,6) (4,3) (4,6) (6,3) (6,6) (3,2) (3,4) (3,6) (6,2) (6,4)}<\/p>\n<p>n (E) = 11<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 11 \/ 36<\/p>\n<p><strong>(viii)<\/strong>&nbsp;Let E be the event of getting neither 9 or 11 as the sum<\/p>\n<p>E = {(3,6) (4,5) (5,4) (5,6) (6,3) (6,5)}<\/p>\n<p>n (E) = 6<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 6 \/ 36<\/p>\n<p>= 1\/6<\/p>\n<p><strong>(ix)<\/strong>&nbsp;Let E be the event of getting sum less than 6<\/p>\n<p>E = {(1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (3,1) (3,2) (4,1)}<\/p>\n<p>n (E) = 10<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 10 \/ 36<\/p>\n<p>= 5\/18<\/p>\n<p><strong>(x)<\/strong>&nbsp;Let E be the event of getting sum less than 7<\/p>\n<p>E = {(1,1) (1,2) (1,3) (1,4) (1,5) (2,1) (2,2) (2,3) (2,4) (3,1) (3,2) (3,3) (4,1) (4,2) (5,1)}<\/p>\n<p>n (E) = 15<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 15 \/ 36<\/p>\n<p>= 5\/12<\/p>\n<p><strong>(xi)<\/strong>&nbsp;Let E be the event of getting more than 7<\/p>\n<p>E = {(2,6) (3,5) (3,6) (4,4) (4,5) (4,6) (5,3) (5,4) (5,5) (5,6) (6,2) (6,3) (6,4) (6,5) (6,6)}<\/p>\n<p>n (E) = 15<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 15 \/ 36<\/p>\n<p>= 5\/12<\/p>\n<p><strong>(xii)<\/strong>&nbsp;Let E be the event of getting neither a doublet nor a total of 10<\/p>\n<p>E\u2032 be the event that either a double or a sum of ten appears<\/p>\n<p>E\u2032 = {(1,1) (2,2) (3,3) (4,6) (5,5) (6,4) (6,6) (4,4)}<\/p>\n<p>n (E\u2032) = 8<\/p>\n<p>P (E\u2032) = n (E\u2032) \/ n (S)<\/p>\n<p>= 8 \/ 36<\/p>\n<p>= 2\/9<\/p>\n<p>So, P (E) = 1 \u2013 P (E\u2032)<\/p>\n<p>= 1 \u2013 2\/9<\/p>\n<p>= 7\/9<\/p>\n<p><strong>(xiii)<\/strong>&nbsp;Let E be the event of getting odd number on first and 6 on second<\/p>\n<p>E = {(1,6) (5,6) (3,6)}<\/p>\n<p>n (E) = 3<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 3 \/ 36<\/p>\n<p>= 1\/12<\/p>\n<p><strong>(xiv)<\/strong>&nbsp;Let E be the event of getting greater than 4 on each die<\/p>\n<p>E = {(5,5) (5,6) (6,5) (6,6)}<\/p>\n<p>n (E) = 4<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 4 \/ 36<\/p>\n<p>= 1\/9<\/p>\n<p><strong>(xv)<\/strong>&nbsp;Let E be the event of getting total of 9 or 11<\/p>\n<p>E = {(3,6) (4,5) (5,4) (5,6) (6,3) (6,5)}<\/p>\n<p>n (E) = 6<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 6 \/ 36<\/p>\n<p>= 1\/6<\/p>\n<p><strong>(xvi)<\/strong>&nbsp;Let E be the event of getting total greater than 8<\/p>\n<p>E = {(3,6) (4,5) (4,6) (5,4) (5,5) (5,6) (6,3) (6,4) (6,5) (6,6)}<\/p>\n<p>n (E) = 10<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 10 \/ 36<\/p>\n<p>= 5\/18<\/p>\n<p><strong>4. In a single throw of three dice, find the probability of getting a total of 17 or 18<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given: The dices are thrown.<\/p>\n<p>By using the formula,<\/p>\n<p>P (E) = favourable outcomes \/ total possible outcomes<\/p>\n<p>The total number of possible outcomes is 6<sup>3<\/sup>=216<\/p>\n<p>So, n (S) = 216<\/p>\n<p>Let E be the event of getting a total of 17 or 18<\/p>\n<p>E = {(6, 6, 5) (6, 5, 6) (5, 6, 6) (6, 6, 6)}<\/p>\n<p>n (E) = 4<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 4 \/ 216<\/p>\n<p>= 1\/54<\/p>\n<p><strong>5. Three coins are tossed together. Find the probability of getting:<br>(i) exactly two heads<br>(ii) at least two heads<br>(iii) at least one head and one tail<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given: Three coins are tossed together.<\/p>\n<p>By using the formula,<\/p>\n<p>P (E) = favourable outcomes \/ total possible outcomes<\/p>\n<p>Total number of possible outcomes is 2<sup>3&nbsp;<\/sup>= 8<\/p>\n<p><strong>(i)<\/strong>&nbsp;Let E be the event of getting exactly two heads<\/p>\n<p>E = {(H, H, T) (H, T, H) (T, H, H)}<\/p>\n<p>n (E) = 3<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 3 \/ 8<\/p>\n<p><strong>(ii)<\/strong>&nbsp;Let E be the event of getting at least two heads<\/p>\n<p>E= {(H, H, T) (H, T, H) (T, H, H) (H, H, H)}<\/p>\n<p>n (E)=4<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 4 \/ 8<\/p>\n<p>= \u00bd<\/p>\n<p><strong>(iii)<\/strong>&nbsp;Let E be the event of getting at least one head and one tail<\/p>\n<p>E = {(H, T, T) (T, H, T) (T, T, H) (H, H, T) (H, T, H) (T, H, H)}<\/p>\n<p>n (E) = 6<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 6 \/ 8<\/p>\n<p>= \u00be<\/p>\n<p><strong>6. What is the probability that an ordinary year has 53 Sundays?<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given: A year which includes 52 weeks and one day.<\/p>\n<p>By using the formula,<\/p>\n<p>P (E) = favourable outcomes \/ total possible outcomes<\/p>\n<p>So, we now have to determine the probability of that one day being Sunday<\/p>\n<p>The total number of possible outcomes is 7<\/p>\n<p>n(S) = 7<\/p>\n<p>E = {M, T, W, T, F, S, SU}<\/p>\n<p>n (E) = 1<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 1 \/ 7<\/p>\n<p><strong>7. What is the probability that a leap year has 53 Sundays and 53 Mondays?<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given: A leap year which includes 52 weeks and two days<\/p>\n<p>By using the formula,<\/p>\n<p>P (E) = favourable outcomes \/ total possible outcomes<\/p>\n<p>So, we now have to determine the probability of that remaining two days is Sunday and Monday<\/p>\n<p>S = {MT, TW, WT, TF, FS, SSu, SuM}<\/p>\n<p>n (S) = 7<\/p>\n<p>E= {SuM}<\/p>\n<p>n (E) = 1<\/p>\n<p>P (E) = n (E) \/ n (S)<\/p>\n<p>= 1 \/ 7<\/p>\n<p><strong>Probability Ex 33.3 Q8<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8583\/16112881045_98ff8798e5_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-45\" width=\"353\" height=\"243\"><br><strong>Probability Ex 33.3 Q9<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8666\/16112885925_ff3f83144a_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-9\" width=\"490\" height=\"212\"><br><strong>Probability Ex 33.3 Q10<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7462\/16112885885_b91cf0ae09_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-10\" width=\"577\" height=\"206\"><br><strong>Probability Ex 33.3 Q11<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7475\/16110992291_416ed094ed_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-11\" width=\"641\" height=\"617\"><br><img src=\"https:\/\/farm8.staticflickr.com\/7484\/15925484048_5513f4b9e0_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-11 i\" width=\"627\" height=\"636\"><br><img src=\"https:\/\/farm8.staticflickr.com\/7513\/15925484008_699575701d_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-11 ii\" width=\"438\" height=\"488\"><br><img src=\"https:\/\/farm8.staticflickr.com\/7469\/16112885825_0b785508ed_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-11 iii\" width=\"598\" height=\"371\"><br><strong>Probability Ex 33.3 Q12<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7495\/15926839109_4cc4a4f43d_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-12\" width=\"468\" height=\"313\"><br><strong>Probability Ex 33.3 Q13<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7539\/15925604060_517cf64fed_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-13\" width=\"592\" height=\"384\"><br><strong>Probability Ex 33.3 Q14<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8657\/15490583294_b8c26e5fef_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-14\" width=\"561\" height=\"215\"><br><strong>Probability Ex 33.3 Q15<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7464\/16110991551_dceef822ab_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-15\" width=\"602\" height=\"411\"><br><strong>Probability Ex 33.3 Q16<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8672\/16112885065_f37b591d45_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-16\" width=\"496\" height=\"546\"><br><img src=\"https:\/\/farm9.staticflickr.com\/8681\/15927149447_524c5cc18c_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-16 i\" width=\"542\" height=\"546\"><br><strong>Probability Ex 33.3 Q17<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7565\/16110991191_abb124053e_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-17\" width=\"489\" height=\"616\"><br><strong>Probability Ex 33.3 Q18<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7470\/16112884775_5d3e2ea795_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-18\" width=\"550\" height=\"545\"><br><strong>Probability Ex 33.3 Q19<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7468\/15925482938_216cec08aa_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-19\" width=\"448\" height=\"220\"><br><strong>Probability Ex 33.3 Q20<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8630\/15925479378_b6c644b5ab_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-44\" width=\"362\" height=\"172\"><br><strong>Probability Ex 33.3 Q21<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8680\/16087114876_ef5f71cca3_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-21\" width=\"517\" height=\"444\"><br><img src=\"https:\/\/farm9.staticflickr.com\/8638\/16087115036_4441d02d84_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-21 i\" width=\"649\" height=\"425\"><br><strong>Probability Ex 33.3 Q22<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7481\/16112170052_f352df5785_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-22\" width=\"319\" height=\"171\"><br><strong>Probability Ex 33.3 Q23<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7527\/15493207873_def8312d54_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-23\" width=\"512\" height=\"192\"><br><strong>Probability Ex 33.3 Q24<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7527\/16087114496_23bfe698a7_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-24\" width=\"375\" height=\"176\"><br><strong>Probability Ex 33.3 Q25<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7578\/15926834739_baaaf90e3c_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-43\" width=\"608\" height=\"412\"><br><strong>Probability Ex 33.3 Q26<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7519\/16112169432_0a268dfb74_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-26\" width=\"394\" height=\"166\"><br><strong>Probability Ex 33.3 Q27<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7481\/15925601950_65e9c0100a_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-27\" width=\"352\" height=\"269\"><br><strong>Probability Ex 33.3 Q28<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7517\/15927147667_82393aa9e1_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-28\" width=\"419\" height=\"469\"><br><strong>Probability Ex 33.3 Q29<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8626\/15925601780_8d88b316a5_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-29\" width=\"530\" height=\"542\"><br><strong>Probability Ex 33.3 Q30<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7524\/16112883225_eed13dba13_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-30\" width=\"444\" height=\"458\"><br><strong>Probability Ex 33.3 Q31<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8572\/15927147257_f415ac6179_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-31\" width=\"377\" height=\"273\"><br><strong>Probability Ex 33.3 Q32<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7550\/16112168612_140b27f290_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-32\" width=\"546\" height=\"281\"><br><strong>Probability Ex 33.3 Q33<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7498\/15490580654_fbb366ddc4_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-33\" width=\"526\" height=\"222\"><br><strong>Probability Ex 33.3 Q34<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7500\/15493206313_3b50c6e6bd_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-34\" width=\"540\" height=\"467\"><br><img src=\"https:\/\/farm9.staticflickr.com\/8657\/16112168292_e09ec6396b_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-34 i\" width=\"518\" height=\"415\"><br><strong>Probability Ex 33.3 Q35<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8610\/16112882505_43a0e94007_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-35\" width=\"385\" height=\"612\"><br><strong>Probability Ex 33.3 Q36<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7571\/15926835739_0e66022be4_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-36\" width=\"399\" height=\"312\"><br><strong>Probability Ex 33.3 Q37<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7506\/15925600680_46e594bb07_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-37\" width=\"469\" height=\"457\"><br><strong>Probability Ex 33.3 Q38<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7517\/15926835339_84484b53b4_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-38\" width=\"501\" height=\"389\"><br><img src=\"https:\/\/farm8.staticflickr.com\/7501\/15926835409_ab1e52bd88_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-38 i\" width=\"367\" height=\"307\"><br><strong>Probability Ex 33.3 Q39<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7564\/15927146117_746202893d_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-39\" width=\"417\" height=\"554\"><br><img src=\"https:\/\/farm9.staticflickr.com\/8667\/15493205603_a5c54afc5d_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-39 i\" width=\"391\" height=\"321\"><br><strong>Probability Ex 33.3 Q40<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8665\/15490579544_02c1b5e3cc_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-40\" width=\"376\" height=\"204\"><br><strong>Probability Ex 33.3 Q41<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7579\/16112881575_fc2b97a7b2_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-41\" width=\"579\" height=\"244\"><br><strong>Probability Ex 33.3 Q42<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7526\/15925599990_5cf052aba6_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-42\" width=\"438\" height=\"498\"><br><strong>Probability Ex 33.3 Q43<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7582\/15925604460_6d15b1b62a_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-8\" width=\"568\" height=\"214\"><br><strong>Probability Ex 33.3 Q44<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8629\/15493208313_d92c89a1c4_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-20\" width=\"443\" height=\"244\"><br><strong>Probability Ex 33.3 Q45<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7510\/15925602210_d5d23450c0_o.png\" alt=\"RD-Sharma-class-11 Solutions-Chapter-33-Probability-Ex-33.3-Q-25\" width=\"384\" height=\"241\"><\/p>\n<p>We have provided complete details of RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3. If you have any queries related to <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\"><strong>CBSE<\/strong><\/a>&nbsp;Class 11, feel free to ask us in the comment section below.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-solutions-class-11-maths-chapter-33-exercise-333\"><\/span>FAQs on RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1630320315781\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-many-questions-are-there-in-rd-sharma-solutions-class-11-maths-chapter-33-exercise-333\"><\/span>How many questions are there in RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>There are a total of 45 questions in RD Sharma Solutions for Class 11 Maths Chapter 33 Exercise 33.3.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630320370958\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-advantages-of-using-rd-sharma-solutions-class-11-maths-chapter-33-exercise-333\"><\/span>What are the advantages of using RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Referring to RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3 will provide students a good understanding of the type of questions that might be asked in the Class 11 exam from the chapter.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630320513952\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-download-rd-sharma-solutions-class-11-maths-chapter-33-exercise-333-free-pdf\"><\/span>Where can I download RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3 free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can download RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3 free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 11 Maths Chapter 33 Exercise 33.3:&nbsp;It is based on a set of axioms. Experts&#8217; key objective is to provide RD Sharma Class 11 Solutions and thereby assist students, regardless of their intelligence level. To assist them in performing well on the board exams, the solutions are described and solved in easy &#8230; <a title=\"RD Sharma Class 11 Solutions Chapter 33 Probability Exercise 33.3 (Updated for 2024)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-33-exercise-33-3\/\" aria-label=\"More on RD Sharma Class 11 Solutions Chapter 33 Probability Exercise 33.3 (Updated for 2024)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":121470,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3428,73334,73564,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68138"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/238"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=68138"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68138\/revisions"}],"predecessor-version":[{"id":515130,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68138\/revisions\/515130"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/121470"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=68138"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=68138"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=68138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}