LEVEL-I
1. From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers, four persons are selected at random. The probability that the selection contains at least one of each
category is
(A) 1/2 (B) 2/3
(C) 2/3 (D) none of these
2. If one ball is drawn at random from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls then the probability that 2 white and 1 black balls will be drawn is
(A) 13/32 (B) 1/4
(C) 1/32 (D) 3/16
3. The probability of occurrence of a multiple of 2 on a dice and a multiple of 3 on the other dice of both are thrown together is
(A) 7/26 (B) 1/32
(C) 11/36 (D) 1/4
4. A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing on the fifth toss equals
(A) 31/32 (B) 1/32
(C) 1/2 (D) 1/5
5. Let A and B be two independent events such that their probabilities are 3/10 and 2/5. The probability of exactly one of the events happening is
(A) 23/50 (B) 1/2
(C) 31/50 (D) none of these
6. A second-order determinant is written down using the numbers 1, –1 as elements. Then the probability for which determinant is non-zero is
(A) 3/8 (B) 5/8
(C) 1/8 (D) 1/2
7. There are 7 seats in a row. Three persons take seats at random. The probability that the middle seat is always occupieace and no two persons are consecutive is
(A) 9/70 (B) 9/35
(C) 4/35 (D) none of these
10. A fair die is thrown until a score of less than 5 points is obtained. The probability of obtaining not less than 2 points on the last thrown is
(A) 3/4 (B) 5/6 (C) 4/5 (D) 1/3
11. Let 'E' and 'F' be two independent events. The probability that both 'E’ and 'F’ happen is 1/12 and the probability that neither 'E' nor 'F' happens is 1/2, then ,
(A) P(E) = 1/3, P(F) = 1/4 (B) P(E) = 1/2, P(F) = 1/6
(C) P(E) = 1/6, P(F) = 1/2 (D) P(E) = 1/4, P(F) = 1/3
ANSWERS
LEVEL −I
1. A
2. A
3. C
4. C
5. A
7. D
8. A
9. C
10. A
11. A
12. B
13. B
14. A
15. B
16. C
17. D
18. B
19. A
20. D
24. B
LEVEL-II
1. All the spades are taken out from a pack of cards. From these cards, cards are drawn one by one with out replacement till the ace of spades comes. The probability that the ace comes in the 4th draw is
(A) 1/13 (B) 12/13
(C) 4/13 (D) none of these
3. A number of six digits is written down at random. Probability that sum of digits of the number is even is
(A)1/2 (B) 3/8 (C) 3/7 (D) none of these
4. Fifteen coupons are numbered 1, 2, 3, - - - 15. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on the selected coupon is 9, is
ANSWERS
LEVEL −II
1. A
2. C
3. A
4. D
5. B
6. D
7. C
8. C
9. C
10. C
11. C
12. B
13. B
14. C
15. C
16. C
17. C
18. B
ANSWERS
LEVEL −III
1. C
2. C
3. B
4. A
