11. A business man is expecting two telephone calls. Mr Walia may call any time between 2 p.m and 4 p.m. while Mr Sharma is equally likely to call any time between 2.30 p.m. and 3.15 p.m. The probability that Mr Walia calls before Mr Sharma is

(A) 1/18

(B) 1/6

(C) 1/6

(D) none of these

12. Let A, B, C be three events such that A and B are independent and P(C) = 0, then events A, B, C are

(A) independent

(B) pairwise independent but not totally independent

(C) P(A) = P(B) = P(C)

(D) none of these

13. In a bag there are 15 red and 5 white balls. Two balls are chosen at random and one is found to be red. The probability that the second one is also red is

(A)12/19

(B)13/19

(C)14/19

(D)15/19

14. A die is thrown a fixed number of times. If probability of getting even number 3 times is same as the probability of getting even number 4 times, then probability of getting even number exactly once is

(A) 1/4

(B) 3/128

(C) 5/64

(D) 7/128

15. A man is know to speak the truth 3 out if 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is

(A) 3/8

(B) 1/5

(B) 3/4

(D) None of these

16. A student appears for test I, II and III. The student is successful if he passes either in test I, II or I, III. The probability of the student passing in test I, II and III are respectively p. q and 1/2. If the probability of the student to be successful is 1/2 then

(A) p = q = 1

(B) p = q = 1/2

(C) p = 1, q = 0

(D) p = 1, q = 1/2

17. Three of six faces of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equal to

(A)1/2

(B)1/5

(C)1/10

(D)1/20

18. A fair coin is tossed repeatedly. If tail appear on 1st four tosses, then the probability of head appearing on 5th toss equals to

(A)1/2

(B)1/32

(C)31/32

(D)1/5

19. A number is chosen at random from the numbers 10 to 99. By seeing the number a man will laugh if product of the digits is 12. If he choose three numbers with replacement then the probability that he will laugh at least once is

(A) 1 –(3/5)^{3}

(B) (43/45)^{3}

(C) 1 –(4/25)^{3}

(D) 1 –(43/45)^{3}

20. If two events A and B are such that P (A) > 0 and P (B) 1, then P is equal to

(A) 1 – P (A/B)

(B) 1 – P(A’/B)

(C) 1 – P [(AUB)/B’]

(D) P (A/B’)

**Answer :**

11. C 12. A 13. C

14. D 15. A 16. C

17. C 18. A

19. D 20. C