**CBSE SAMPLE PAPER**

**Maths Sample Paper for Class XII**

**Topic – PROBABILITY**

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**Time : 90 min**

- 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.
- 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?
- 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.
- 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

- 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

- 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?
- 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.
- 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.
- 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.
- 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?
- 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.
- 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?
- 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.
- 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.
- If P(A) = 0.4, P(B) =0.8, P(B/A) = 0.6, find P(A/B) and P(A U B)