Page 270 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 12: Probability and Expected Value

8. Two cards are drawn at random from a pack of 52 cards. What is the probability that the Notes
first is a king and second is a queen?
9. What is the probability of successive drawing of an ace, a king, a queen and a jack from a
pack of 52 well shuffled cards? The drawn cards are not replaced.
10. 5 unbiased coins with faces marked as 2 and 3 are tossed. Find the probability of getting a
sum of 12.
11. If 15 chocolates are distributed at random among 5 children, what is the probability that a
particular child receives 8 chocolates?

12. A and B stand in a ring with 10 other persons. If arrangement of 12 persons is at random,
find the chance that there are exactly three persons between A and B.
13. Two different digits are chosen at random from the set 1, 2, 3, 4, 5, 6, 7, 8. Find the
probability that sum of two digits exceeds 13.
14. 5-letter words are formed from the letters of the word ORDINATES. What is the probability
that the word so formed consists of 2 vowels and 3 consonants?
15. Maximum number of different committees are formed out of 100 teachers, including
principal, of a college such that each committee consists of the same number of members.
What is the probability that principal is a member of any committee?
16. If n persons are seated around a round table, find the probability that in no two ways a
man has the same neighbours.
17. 6 teachers, of whom 2 are from science, 2 from arts and 2 from commerce, are seated in a
row. What is the probability that the teachers of the same discipline are sitting together?

18. A problem in economics is given to 3 students whose chances of solving it are and
respectively. What is the probability that the problem will be solved?
19. What is the chance that a non-leap year selected at random will contain 53 Sundays?

20. Two men M and M and three women W , W and W , in a big industrial firm, are trying
1 2 1 2 3
for promotion to a single post which falls vacant. Those of the same sex have equal
probabilities of getting promotion but each man is twice as likely to get the promotion as
any women.
(a) Find the probability that a woman gets the promotion.

(b) If M and W are husband and wife, find the probability that one of them gets the
2 2
promotion.
Answers: Self Assessment

1. True 2. True

3. True 4. True
5. False 6. True
7. True 8. True
9. constant itself 10. expected monetary value
11. E(X) + E(Y). 12. (a)

13. (c) 14. (a)
15. (b) 16. (d)

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