PROBABILTY DPP 1
1) A box contains 6 red and 4 blue balls. Two balls are drawn without replacement. The
second ball drawn is red’ has probability p/q. (p and q are
co-prime), then value of p + q is -
(A) 10 (B) 8 (C) 5 (D) 4
2) Consider a set 'P' containing 'n' elements. A subset 'A' of 'P' is drawn and there after set 'P'
is reconstructed. Now one more subset 'B' of 'P' is drawn. Probability of drawing sets A and B
so that A B has exactly one element –
A) (3/4)n.n (B) n.(3/4)n – 1 [B]
(C) n.(3/4)n (D) None of these
3) A letter is known to have come from either TATANAGAR or CALCUTTA. On the
envelope, just two consecutive letters TA are visible . The probability that the letter has come
from CALCUTTA is
(A) 4/11 (B) 1/3 [A]
(C) 5/12 (D) None of these
4) Probability that a randomly drawn card from a pack of playing cards is either a spade
| a 3|
or a queen is . Then -
13
(A) a = 0 (B) a = 7 [B]
(C) a = 4 (D) a = 5
5) A can hit a target 4 times in 5 shots, B can hit the same 3 times in 4 shots and C twice
in 3 shots. If they fire one each, the probability that at least of them hit the target is-
(A) 5/6 (B) 11/12
(C) 9/10 (D) None of these
6) If A and B are two events such that P(A) > 0 and P(B) 1 then P( A / B ) is equal to-
A A 1 P (A B) P(A )
(A) 1 – P (B) 1 – P (C) (D)
B B P ( B) P ( B)
7) If two events A and B are such that P(AC) = 0.3, P(B) = 0.4 and P(ABC) = 0.5 then
P[B/(A BC)] is equal to-
1 1 3 2
(A) (B) C) (D)
4 2 4 3
8) Two persons A and B throw a die alternately till one of them get a “six” and wins the
game. The probability of winning of B is-
6 5 3
(A) (B) (C) (D) None of these
11 11 11
9) The chance that the vowels are separated in an arrangement of the letters of the word
“HORROR” is :
(A) 1/2 (B) 2/3 (C) 3/4 (D) none
6 5 4
10) If for two events A, B ; P (A B) = ,P(A)= , P(B) = , then A, B are
7 7 7
(A) independent events (B) mutually exclusive
(C) equally likely (D) forming an exhaustive system
11) What is the probability that the two squares chose randomly on a chess board, share a side -
(A) 1/18 (B) 13/254
(C) 105/288 (D) 13/96
12) Three person A1, A2, A3 are to speak at a function along with 5 other persons. If the person
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
13) A pair of unbiased dice are rolled together till a sum of either 5 or 7 is obtained. The
probability that 5 comes before 7 is
(A) 2/5 (B) 3/5
(C) 4/5 (D) none of these
14) Three critics review a book. Odds in favour of the book are 5 : 2, 4 : 3 and 3 : 4 respectively
for the three critics. The probability that majority are in favour of the book is
35 125
(A) (B)
49 343
164 209
(C) (D)
343 343
15) Three six-faced dice are thrown together. The probability that the sum of the numbers
appearing on the dice is k (9 k 14), is -
21k k 2 83 k 2 3k 2
(A) (B)
216 432
21k k 2 83
(C) (D) None of these
432
1 2
16) If A and B are two events such that P(A) = and P(B) = , then -
2 3
1 1
(A) P (A B) (B) P (A B )
3 2
1 1 1 3
(C) P(A B) (D) P( A B)
6 2 6 4
17) A determinant is chosen at random from the set of all determinants of order 2 with elements 0
or 1 only. The probability that the determinant chosen is non-zero is -
3 3 1
(A) (B) (C) (D) None of these
16 8 4
18) Four numbers are multiplied together. Then the probability that the product will be divisible
by 5 or 10 is -
369 399 123 133
(A) (B) (C) (D)
625 625 625 625
19) A, B, C are events such that P (A) = 0.3,
P (B) = 0.4, P (C) = 0.8, P (A B) = 0.08, P ( A C ) = 0.28, P (A B C) = 0.09.
If P (A B C) 0.75, then P (B C) lies in the interval -
(A) (0.23, 0.48) (B) (0.2, 0.4) (C) (0.25, 0.50) (D) None of these
20) Out of 21 tickets marked with numbers 1, 2,…. , 21, three are drawn at random without
replacement. The probability that these numbers are in A.P. is -
10 9 14 13
(A) (B) (C) (D)
133 15 261 261
21) A student appears for tests I, II and III. The student is successful if he passes either in
tests I and II or tests I and III. The probabilities of the student passing in tests I, II, III are
p, q and 1/2, respectively. If the probability that the student is successful is 1/2, then
possible value of p and q are -
(A) p = q = 1 (B) p = q = 1/2 (C) p = 1, q = 0 (D) p = 1, q = 1/2
22) Consider the Cartesian plane R2 and Let X denote the subset of points for which both
coordinate are integer. A coin of diameter 1/2 is tossed randomly onto the plane. The
probability p that the coin covers a point of X -
(A) 0.2 (B) 0.8 (C) 1.2 (D) None of these
23) A person writes 4 letters and addresses 4 envelopes. If the letters are placed in the
envelopes at random, the probability that not all letters are placed in correct envelopes
is -
(A) 1/24 (B) 11/24 (C) 5/8 (D) 23/24
24) If p and q are chosen from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, with replacement, the
probability that the roots of the equation x2 + 2px + q = 0 are real is-
(A) 0.84 (B) 0.16 (C) 0.62 (D) 0.38
25) A can hit a target 4 times in 5 shots, B three times in 4 shots and C twice in 3 shots. They
fire a target if exactly two of them hit the target then the chance that it is C who has
missed is
6 1 4 4
(A) (B) (C) (D)
13 5 5 15
26) Let F denote the set of all onto functions from A = {a1, a2, a3, a4} to B = {x, y, z}. A function f is
chosen at random from F. The probability that f –1 (x) consists of exactly two elements is
(A) 2/3 (B) 1/3 (C) 1/6 (D) 0
27) From a well shuffled pack of 52 playing cards, if cards are drawn one by one without
replacement till the black ace comes, then probability that the black aces comes in the
4th draw is -
25 89
(A) (B)
52 245
24 93
(C) (D)
663 256
28) Let 0 < P (A) < 1, 0 < P (B) < 1 and P (A B) = P (A) + P (B) – P (A) P (B), then -
(A) P (A | B) = 0
(B) P (B | A) = 0
(C) P (A B) = P (A) P (B)
(D) P (A | B) + P (B | A) = 1
29) India play two matches each with West Indies and Australia. In any match the probabilities of
India getting 0, 1 and 2 points are 0.45, 0.05 and 0.50 respectively. Assuming that the
outcomes are independent, the probability of India getting at least 7 points, is -
(A) 0.0875 (B) 1/16
(C) 0.1125 (D) None of these
30) A speaks truth in 80% cases and B in 60% cases. In what percentage of case are they likely to
contradict each other in starting the same fact :
(A) 44% (B) 56%
(C) 42% (D) 48%
31) For any two events A and B in a sample
space -
P(A) P(B) 1
(A) P(A/B) ,
P(B)
P(B) 0 is always true
(B) P (A B ) = P(A) – P (A B)
does not hold
(C) P (A B) = 1 – P( A ) P( B ),
if A and B are independent.
(D) P (A B) = 1 – P( A ) P( B ),
if A and B are disjoint.
BY ASHISH SIR
