#### Introduction To Probability Theory Book Back Questions

11th Standard

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. Four persons are selected at random from a group of 3 men, 2 women, and 4 children. The probability that exactly two of them are children is

(a)

${3\over4}$

(b)

${10\over23}$

(c)

${1\over2}$

(d)

${10\over21}$

2. Two items are chosen from a lot containing twelve items of which four are defective, then the probability that at least one of the item is defective

(a)

${19\over 33}$

(b)

${17\over 33}$

(c)

${23\over 33}$

(d)

${13\over 33}$

3. A matrix is chosen at random from a set of all matrices of order 2, with elements 0 or 1 only. The probability that the determinant of the matrix chosen is non zero will be

(a)

${3\over 16}$

(b)

${3\over 8}$

(c)

${1\over 4}$

(d)

${5\over 8}$

4. If two events A and B are independent such that P(A)=0.35 and $P(A\cup B)=0.6$ ,then P(B) is

(a)

${5\over 13}$

(b)

${1\over 13}$

(c)

${4\over 13}$

(d)

${7\over 13}$

5. There are three events A, B, and C of which one and only one can happen. If the odds are 7 to 4 against A and 5 to 3 against B, then odds against C is

(a)

23: 65

(b)

65: 23

(c)

23: 88

(d)

88: 23

6. 3 x 2 = 6
7. A man has 2 ten rupee notes, 4 hundred rupee notes and 6 five hundred rupee notes in his pocket. If 2 notes are taken at random, what are the odds in favour of both notes being of hundred rupee denomination and also its probability

8. A single card is drawn from a pack of 52 cards. What is the probability that
The card will be 6 or smaller?

9. Suppose P(B) = $\frac {2 }{ 5 }$ Express the odds that the event B occurs

10. 3 x 3 = 9
11. One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that (i) both are white (ii) both are black (iii) one white and one black.

12. A die is thrown twice. Let A be the event, ‘First die shows 5’ and B be the event 'second die shows 5’. Find $P(A\cup B)$ .

13. The probability that a girl, preparing for competitive examination will get a State Government service is 0.12, the probability that she will get a Central Government job is 0.25, and the probability that she will get both is 0.07. Find the probability that (i) she will get atleast one of the two jobs (ii) she will get only one of the two jobs.

14. 2 x 5 = 10
15. Can two events be mutually exclusive and independent simultaneously?

16. A coin is tossed twice. Events E and F are defined as follows
E= Head on first toss, F = Head on second toss. Find.
(i) P(E$\cup$F)
(ii) P(E/F)
(iii) $P(\bar { E } /F)$
(iv) Are the events E and F independent