CBSE Class 12 Mathematics Probability MCQs Set 02

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