1 . Three persons A1, A2 and A3 are to speak at a function along with 5 other persons. If the persons speak in random order, the probability that A1 speaks before A2 and A2 speaks before A3 is

(A) 1/6

(B) 3/5

(C) 3/8

(D) none of these

2. Two persons A, and B, have respectively n + 1 and n coins, which they toss simultaneously. Then probability P that A will have more heads than B

(A) P >1/2

(B) P = 1/2

(C) 1/4 < P < 1/2

(D) 0 < P < 1/4

3. On a toss of two dice, A throws a total of 5, then the probability that he will throw another 5 before he throws 7, is

(A) 1/9

(B) 1/6

(C) 2/5

(D) 5/36

4. One of two events must occur. If the chance of one is of the other, then odd in favor of the other are

(A) 1 : 3

(B) 3 : 1

(C) 2 : 3

(D) none of these

5. In a convex polygon of 6 sides two diagonals are selected at random. The probability that they intersect at an interior point of the polygon is

(A)2/5

(B)5/12

(C)7/12

(D)3/5

6. A and B are two events such that P(A) = 0.2 and P(A∪B) = 0.7. If A and B are independent events then P(B’) equals

(A) 2/7

(B) 7/9

(C) 3/8

(D) none of these

7. A fair coin is tossed 99 times. Let X be the number of times heads occurs. Then P(X=r) is maximum when r is

(A) 49

(B) 52

(C) 51

(D) None of these

8. The numbers 1, 2, 3,…, n are arranged in random order. The probability that the digits 1, 2, 3…k (k < n) appear as neighbours in that order is

(A) 1/n!

(B) k!/n!

(C) (n-k)!/n!

(D) None of these

9. Entries of a 2 x 2 determinant are chosen from the set {1, 1}. The probability that determinant has zero value is

(A) 1/4

(B) 1/3

(C) 1/2

(D) none of these

10. A bag contains 14 balls of two colours, the number of balls of colour being equal, seven balls are drawn at random one by one. The ball in hand is returned to the bag before each new draw. The probability that at least 3 balls of each colour are drawn, is

(A) 1/2

(B) >1/2

(C) < 1/2

(D) none of these

**Answer :**

1. (A) 2. (B) 3. (C) 4. (D) 5. (B)

6. (C) 7. (A) 8. (D) 9. (C) 10. (A)

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)