CBSE Class 12 Mathematics Probability MCQs Set B

Question. Two dice are rolled one after the other. The probability that the number on the first is smaller than the number on the second is
(a) 1/2
(b) 7/18
(c) 3/4
(d) 5/12

Answer : D

Question. On hundred cards are numbered from 1 to 100. The probability that a randomly chosen card has a digit 5 is
(a) 1/100
(b) 9/100
(c) 19/100
(d) None of the options

Answer : C

Question. Odds in favour of an event A are 2 to 1 and odds in favour of A∪ B are 3 to 1. Consistent with this information the smallest and largest values for the probability of event B are given by
(a)1/6≤P(B) ≤ 1/3
(b) 1/3≤p(B) ≤ 1/2
(c) 1/12≤p(B)≤ 3/4
(d) None of the options

Answer : C

Question. A car is parked by a driver amongst 25 cars in a row, not at either end. When he returns he finds that 10 places are empty. The probability that both the neighbouring places of driver’s car are vacant, is
(a) 9/92
(b) 15/92
(c) 21/92
(d) 27/92

Answer : B

Question. If two events A and B are such that P (Ac)=0.3 p(B)=0.4, ((A∩Bc)= 0.5, then P(B/A∪Bc) is equal to
(a) 0.20
(b) 0.25
(c) 0.30
(d) 0.35

Answer : B

Question. If each element of a second order determinant is zero or one, what is the probability that the values of the determinant is positive?
(a) 3/16
(b) 5/16
(c) 15/16
(d) None of the options

Answer : A

Question.

Answer : C

Question. Ten coins are tossed. Then, the probability of getting atleast 8 heads is
(a) 1/128
(b) 1/256
(c) 7/128
(d) 3/256

Answer : C

Question. Two dice are tossed. The following two events A and B are A x y = {(x,y) : x+y = 11},B= {(x,y): x≠5} where (x,y) denotes a typical sample point.
(a) Not independent
(b) independent
(c) Mutually exclusive
(d) None of the above

Answer : A

Question. Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all the four cards are kings?
(a) 1/725
(b) 1/125
(c) 1/2025
(d) None of the options

Answer : D

Question. The probability that in a group of N (< 365 ) people, at least two will have the same birthday is

Answer : D

Question. If 2P (A) = P(B)= 5/13 and P(A/B) = 2/5, then P(A∪B) is
(a) 11/26
(b) 3/26
(c) 5/26
(d) None of the options

Answer : A

Question. A coin is tossed three times E : at most two tails F : at least one tail, then P(E/F) is
(a) 2/7
(b) 6/7
(c) 1/7
(d) 3/7

Answer : B

Question. Three numbers are chosen at random without replacement from the set A {x|1≤ x ≤ 10,x ∈ N}. The probability that the minimum of the chosen numbers is 3 and maximum is 7, is
(a) 1/12
(b) 1/15
(c) 1/40
(d) 39/40

Answer : C

Question. A black and a red die are rolled, then the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4, is
(a) 1 /3
(b) 1/9
(c) 2/3
(d) 0

Answer : B

Question.

Answer : A

Question. If A and B are any two events such that P(A) + P(B) – P(A and B) = P(A), then
(a) P(B|A) = 1
(b) P(A|B) = 1
(c) P(B|A) = 0
(d) P(B|A) = 0

Answer : B

Question. In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is
(a) 10–1
(b) (1/2)5
(c) (9/10)5
(d) 9/10

Answer : C

Question. Two events E and F are independent. If P(E) = 0.3, P(E ∪ F) = 0.5, then P(E|F) – P(F|E) equals
(a) 2/7
(b) 3/35
(c) 1/70
(d) 1/7

Answer : C

Question. If A and B are two independent events with P(A) = 3/5 and P(B) = 4/5 , then P(A’∩B’) equals
(a) 4/15
(b) 8/45
(c) 1/3
(d) 2/9

Answer : D

Question. If P(A) = 2/5 , P(B) = 3/10 and P(A∩B) = 1/5 , then P(A¢|B¢).P(B’|A’) is equal to
(a) 5/6
(b) 5/7
(c) 25/42
(d) 1

Answer : C

Question. Let P(A) = 7/13 = 9/13 , P(B) and P(A∩B) = . 4/13 Then P(A’/ B) is equal to
(a) 6/13
(b) 4/13
(c) 4/9
(d) 5/9

Answer : B

Question. If P(A|B) > P(A), then which of the following is correct:
(a) P(B|A) < P(B)
(b) P(A∩B) < P(A).P(B)
(c) P(B|A) > P(B)
(d) P(B|A) = P(B)

Answer : C

Question. If P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6, then P(A∪B) is equal to
(a) 0.24
(b) 0.3
(c) 0.48
(d) 0.96

Answer : D

Question. A and B are two students. Their chances of solving a problem correctly are 1/3 and 1/4 , respectively. If the probability of their making a common error is 1/20 and they obtain the same answer, then the probability of their answer to be correct is
(a) 1/12
(b) 1/40
(c) 13/120
(d) 10/13

Answer : D

Question. If P(A) = 4/5 and P(A∩B)= 7/10 , then (P(B|A) is equal to
(a) 1/10
(b) 1/8
(c) 7/8
(d) 17/20

Answer : C

Question. If A and B are two events such that P(A) ≠ 0 and P(B|A) = 1, then
(a) A ⊂ B
(b) B ⊂ A
(c) B = j
(d) A = j

Answer : A

Question. A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is
(a) 3/28
(b) 2/21
(c) 1/28
(d) 167/168

Answer : A
 

Case-based MCQs

I. Read the following text and answer the following questions on the basis of the same:

In answering a question on a multiple choice test for class XII, a student either knows the answer or guesses. Let 3/5 be the probability that he knows the answer and 2/5 be the probability that he guesses.
Assume that a student who guesses at the answer will be correct with probability 1/3 . Let E1, E2, E be the events that the student knows the answer, guesses the answer and answers correctly respectively.

Question. What is the value of P(E1)?
(a) 2/5
(b) 1/3
(c) 1
(d) 3/5

Answer : D

Question. Value of P(E|E1) is
(a) 1/3
(b) 1
(c) 2/3
(d) 4/5

Answer : B

Question. Value of
(a) 1/3
(b) 1/5
(c) 1
(d) 3/5

Answer : C

Question. What is the probability that the student knows the answer given that he answered it correctly?
(a) 2/11
(b) 5/3
(c) 9/11
(d) 13/3

Answer : C
 

II. Read the following text and answer the following questions on the basis of the same:
Anand, Samanyu and Shah of SHORTCUTS classes were given a problem in Mathematics whose respective probabilities of solving it are 1/2 , 1/3 and 1/4. They were asked to solve it independently. (Image 209)

Based on the above data, answer any four of the following questions.

Question. The probability that Anand alone solves it is _______.
(a) 1/4
(b) 3/4
(c) 11/24
(d) 17/24

Answer : A

Question. The probability that the problem is not solved is _______.
(a) 1/4
(b) 3/4
(c) 0
(d) 11/24

Answer : A

Question. The probability that the problem is solved is _______.
(a) 1/4
(b) 3/4
(c) 17/24
(d) 11/24

Answer : B

Question. The probability that exactly one of them solves it is _______.
(a) 1/4
(b) 3/4
(c) 17/24
(d) 11/24

Answer : D

Question. The probability that exactly two of them solves it is _______.
(a) 1/4
(b) 3/4
(c) 17/24
(d) 11/24

Answer : A
 

III. Read the following text and answer the following questions on the basis of the same:
A group of people start playing cards. And as we know a well shuffled pack of cards contains a total of 52 cards. Then 2 cards are drawn simultaneously (or successively without replacement). (Image 208)

Question. If x = no. of kings = 0, 1, 2. Then P(x = 0) = ?
(a) 188/221
(b) 198/223
(c) 197/290
(d) 187/221

Answer : A

Question. If x = no. of kings = 0, 1, 2. Then P(x = 1) = ?
(a) 32/229
(b) 32/227
(c) 32/221
(d) 32/219

Answer : C

Question. If x = no. of kings = 0, 1, 2. Then P(x = 2) = ?
(a) 2/219
(b) 1/221
(c) 3/209
(d) 1/209

Answer : A

Question. Find P(X = 1) + P(X = 2).
(a) 188/221
(b) 1/221
(c) 189/221
(d) 220/221

Answer : C

Question. Find P(x ≥ 1).
(a) 188/221
(b) 1/221
(c) 189/221
(d) 220/221

Answer : D