# CBSE Sample Paper Class XII Maths

CBSE SAMPLE PAPER

Maths Sample Paper for Class XII

Topic – PROBABILITY

Time : 90 min

1. The probability of a student A passing an examination is 2/9 and of student B passing is 5/9. Assuming the two events: ‘A passes’,’B passes independent’, find the probability of: (i) only A passing the examination (ii) only one of them passing the examination.
2. There are three urns A, B and C. Urn A contains 4 red balls and 3 black balls. Urn B contains 5 red balls and 4 black balls. Urn C contains 4 red balls and 4 black balls. One ball is drawn from each of these Urns. What is the probability that three balls drawn consist of 2 red balls and a black ball?
3. A bag contains 6 red balls and 8 black balls and another bag contains 8 red balls and 6 black balls. A ball is drawn from the first bag and without noticing its color is put in the second bag. A ball is drawn from the second bag. Find the probability that the ball drawn is red in color.
4. A bag contains 4 white balls and 2 black balls and another contains 3 white balls and 5 black balls. If one ball is drawn from each bag, find the probability that

(i) both are white

(ii) both are black

(iii) one is white and one is black

1. A husband and wife appear in a interview for two vacancies in the same post. The probability of husband’s selection is 1/7 and that of wife’s selection is 1/5. What is the probability that

(a)   both of them will be selected

(b)   only one of them will be selected

(c)   none of them will be selected

1. Two cards are drawn from a well-shuffled pack of 52 cards, one after another without replacement. Find the probability that one of these is red card and the other a black card?
2. Tickets are numbered from 1to10. Two tickets are drawn one after the other at random. Find the probability that the number on one of the tickets is a multiple of 5 and on the other a multiple of 4.
3. In a family, the husband tells a lie in 30% cases and the wife in 35% cases. Find the probability that both contradict each other on the same fact.
4. An unbiased die is tossed twice. Find the probability of getting 4,5 or 6 on the first toss and 1,2,3, or 4 on the second toss.
5. A dice is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?
6. A bag contains 5 white, 7red and 3 black balls. If three balls are drawn one by one without replacement, find the probability that none is red.
7. A die is thrown twice and the sum of the numbers appearing is observed to be 8. What is the conditional probability that the number 5 has appeared at least once?
8. A bag contains tickets numbered from 1 to 20. Two tickets are drawn. Find the probability that (i) both the tickets have prime numbers on them (ii) on one there is a prime number and on the other there is a multiple of 4.
9. Two persons A and B throw a die alternately till one of them gets a ‘three’ and wins the game. Find their respectively probabilities of winning, if A begins.
10. If P(A) = 0.4, P(B) =0.8, P(B/A) = 0.6, find P(A/B) and P(A U B)