CUET Mathematics MCQs Probability, Multiple Choice Questions (2024)

Question. A bag contains 4 red and 6 black balls. A ball is drawn atrandom from the bag, its colour is observed and this ballalong with two additional balls of the same colour arereturned to the bag. If now a ball is drawn at random fromthe bag, then the probability that this drawn ball is red, is :
(a)2/5
(b)1/5
(c)3/4
(d)3/10
Answer :A

Question. Two aeroplanes I and II bomb a target in succession. Theprobabilities of I and II scoring a hit correctly are 0.3 and0.2, respectively. The second plane will bomb only if thefirst misses the target. The probability that the target is hitby the second plane is
(a) 0.2
(b) 0.7
(c) 0.06
(d) 0.14.
Answer : D

Question. If a fair die is rolling. The events are E={1,3,6}, F={4,6}. Then the probability P(E/F) is
a) 1/2
b) 2/3
c) 1/6
d) None of these
Answer :A

Question. A speaks truth in 75% cases and B speaks truth in 80% cases. The probability that they contradict each other in a statement is
a) 7/20
b) 13/20
c) 3/5
d) 2/5
Answer :A

Question. A player X has a biased coin whose probability of showingheads is p and a player Y has a fair coin. They start playinga game with their own coins and play alternately. The playerwho throws a head first is a winner. If X starts the game,and the probability of winning the game by both the playersis equal, then the value of ‘p’ is
(a)1/3
(b)1
(c)1/4
(d)2/5
Answer :A

Question. Let A and E be any two events with positive probabilities:
Statement - 1: P(E/A) ≥ P(A/E) P(E)
Statement - 2: P(A/E) ≥ P(A∩E)
(a) Both the statements are true
(b) Both the statements are false
(c) Statement-1 is true, Statement-2 is false
(d) Statement-1 is false, Statement-2 is true
Answer :A

Question. Let A, B, C, be pairwise independent events with P (C) > 0and P( A ∩ B ∩ C) = 0. ThenP (A^c∩ B^c / C)
(a) P (B^c) - P (B)
(b) P (A^c) +P (B^c)
(c) P (A^c) - P (B^c)
(d) P (A^c) - P (B)
Answer : D

Question. Let two fair six-faced dice A and B be thrownsimultaneously. If E₁ is the event that die A shows upfour, E₂ is the event that die B shows up two and E₃ is theevent that the sum of numbers on both dice is odd, thenwhich of the following statements is NOT true ?
(a) E₁ and E₃are independent.
(b) E₁, E₂ and E₃ are independent.
(c) E₁ and E₂ are independent.
(d) E₂ and E₃ are independent.
Answer : B

Question. Three houses are available in a locality. Three personsapply for the houses. Each applies for one house withoutconsulting others. The probability that all the three applyfor the same house is
(a)9/2
(b)9/1
(c)9/8
(d)9/7
Answer : B

Question. Let A and B are two events. If P(A)=0.2 p(B)=0.4, P(AᴜB)=0.6, then P(A/B) is equal to
a) 0
b) 0.3
c) 0.5
d) 0.8
Answer :A

Question. The probability that a leap year will have 53 fridays or 53 saturdays
a) 3/7
b) 4/7
c) 1/7
d) 2/7
Answer :A

Question. If A and B are any two events such thatP(A) = 2/5andP(A ∩ B) = 3/20 then the conditional probability,P(A | A' ù B')) , where A' denotes the complement of A, isequal to :
(a) 11/20
(b) 5/17
(c) 8/17
(d) 1/4/5
Answer : B

Question. Let X be a set containing 10 elements and P(X) be itspower set. If A and B are picked up at random from P(X),with replacement, then the probability that A and B haveequal number elements, is :
(a)(210 -1)
(b)²⁰C₁₀/2¹⁰
(c)(2¹⁰ - 1)/2²⁰
(d)²⁰C₁₀/2²⁰
Answer : D

Question. Let a random variable X have a binomial distribution withmean 8 and variance 4. If P(X d” 2) = k/16², then k is equalto:
(a) 17
(b) 121
(c) 1
(d) 137
Answer : D

Question. The probability that A speaks truth is ,5/4while theprobability for B is .4/3
The probability that they contradicteach other when asked to speak on a fact is
(a)5/4
(b)5/1
(c)20/7
(d)20/3
Answer : C

Question. Two numbers are chosen from {1,2,3,4,5,6} one after the other without replacement. The probability that one of the smaller values is less than 4 is
a) 4/5
b) 1/15
c) 1/5
d) 14/15
Answer :A

Question. An unbiased coin is tossed eight times. The probability ofobtaining at least one head and at least one tail is :
(a)255/256
(b)127/128
(c)63/64
(d)1/2
Answer : B

Question. Three persons P, Q and R independently try to hit a target.If the probabilities of their hitting the target are3/4, 1/4and5/8respectively, then the probability that the target is hitby P or Q but not by R is :
(a)21/64
(b)9/64
(c)15/64
(d)39/64
Answer :A

Question. The probability of a man hitting a target is2/5. He fires atthe target k times (k, a given number). Then the minimumk, so that the probability of hitting the target at least onceis more than7/10, is :
(a) 3
(b) 5
(c) 2
(d) 4
Answer :A

Question : A person writes 4 letters and addresses 4 envelopes . If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is
a) 23/24
b) 15/24
c) 11/24
d) 1/4
Answer :A

Question. Let A and B be two events such that P(A)=0.6, P(B)=0.2 and P(A/B)=0.5, then P(A’/B’) equals
a) 3/8
b) 3/10
c) 1/10
d) 6/7
Answer :A

Question. If the probability of hitting a target by a shooter, in anyshot, is1/3then the minimum number of independent shotsat the target required by him so that the probability ofhitting the target at least once is greater than5/6is:
(a) 3
(b) 6
(c) 5
(d) 4
Answer : C

Question. A, B, C try to hit a target simultaneously but independently.
Their respective probabilities of hitting the targets are
3/4, 1/2, 5/8. The probability that the target is hit by A or B butnot by C is :
(a) 21/64
(b) 7/8
(c) 7/32
(d) 9/64
Answer :A

Question. A person throws two fair dice. He wins Rs. 15 for throwinga doublet (same numbers on the two dice), wins Rs. 12when the throw results in the sum of 9, and loses Rs. 6 for
any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :
(a) (1/2) gain
(b) (1/4) loss
(c) (1/2) loss
(d) 2 gain
Answer : C

Question. The probability of a student getting 1,2,3 division in an examination are 1/10, 3/5 and 1/4 respectively. The probability that the student fails in the examination is
a) 27/100
b) 83/100
c) None of these
d) 197/200
Answer :A

Question. Three numbers are chosen at random without replacementfrom {1,2,3,..8}. The probability that their minimum is 3,given that their maximum is 6, is :
(a)3/8
(b)1/5
(c)1/4
(d)2/5
Answer : B

Question. If C and D are two events such that C ⊂D and P(D) ≠ 0,then the correct statement among the following is
(a) P(C | D) ≥ P(C)
(b) P(C | D) < P(C)
(c) P(C | D)= P(D)/P(C)
(d) P(C | D) = P(C)
Answer :A

Question. A die is thrown two times and the sum of the scoresappearing on the die is observed to be a multiple of 4.
Then the conditional probability that the score 4 hasappeared atleast once is :
(a)1/4
(b)1/3
(c)1/8
(d)1/9
Answer : D