CBSE Class 11 Mathematics Probability Worksheet

Question. Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is:
(a) 15/101
(b) 5/101
(c) 5/33
(d) 10/99
Answer : C

Question. If six students, including two particular students A and B, stand in a row, then the probability that A and B are separated with one student in between them is
(a) 8/15
(b) 4/15
(c) 2/15
(d) 1/15
Answer : B

Question. Two different families A and B are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is 1/12, then the number of children in each family is?
(a) 4
(b) 6
(c) 3
(d) 5
Answer : D

Question. If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is :
(a) 965/2¹¹
(b) 965/2¹⁰
(c) 945/2¹⁰
(d) 945/2¹¹
Answer : C

Question. A set S contains 7 elements. A non-empty subset A of S and an element x of S are chosen at random. Then the probability that xÎA is:
(a) 1/2
(b) 64/127
(c) 63/128
(d) 31/128
Answer : B

Question. If three of the six vertices of a regular hexa on are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is :
(a) 1/10
(b) 1/5
(c) 3/10
(d) 3/20
Answer : A

Question. If A and B are two events such that P(A∪B) = P(A∩B) , then the incorrect statement amongst the following statements is:
(a) A and B are equally likely
(b) P(A∩B') = 0
(c) P(A'∩B) = 0
(d) P(A) + P(B) = 1
Answer : D

Question. Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is
(a) 2/5
(b) 4/5
(c) 3/5
(d) 1/5
Answer : A

Question. A number x is chosen at random from the set {1, 2, 3, 4, ...., 100}. Define the event: A = the chosen number x satisfies (x - 10) (x - 50) / (x - 30) ≥ 0
Then P (A) is:
(a) 0.71
(b) 0.70
(c) 0.51
(d) 0.20
Answer : A

Question. There are two balls in an urn. Each ball can be either white or black. If a white ball is put into the urn and there after a ball is drawn at random from the urn, then the probability that it is white is
(a) 1/4
(b) 2/3
(c) 1/5
(d) 1/3
Answer : B

Question. A box 'A' contanis 2 white, 3 red and 2 black balls. Another box 'B' contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box 'B' is
(a) 7/16
(b) 9/32
(c) 7/8
(d) 9/16
Answer : A

Question. Let A and B be two events such that the probability that exactly one of them occurs is 2/5 and the probability that A or B occurs is 1/2, then the probability of both of them occur together is:
(a) 0.02
(b) 0.20
(c) 0.01
(d) 0.10
Answer : D

Question. The probabilities of three events A, B and C are given by P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5. If P (A∪B) = 0.8, P (A∩C) = 0.3, P (A∩B∩C) = 0.2, P (B∩C) = b and P (A∪B∪C) = a, where 0.85 ≤ a ≤ 0.95 , then b lies in the interval:
(a) [0.35, 0.36]
(b) [0.25, 0.35]
(c) [0.20, 0.25]
(d) [0.36, 0.40]
Answer : B

Question. Let X and Y are two events such that P(X ∪ Y ) = P( X ∩ Y ).
Statement 1: P( X ∩ Y ') = P( X '∩ Y ) = 0
Statement 2: P( X) + P(Y) = 2P( X ∩ Y)
(a) Statement 1 is false, Statement 2 is true.
(b) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
(c) Statement 1 is true, Statement 2 is false.
(d) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
Answer : B

Question. In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :
(a) 1/6
(b) 1/3
(c) 2/3
(d) 5/6
Answer : A

Question. Let S = {1, 2, ....., 20}. A subset B of S is said to be “nice”, if the sum of the elements of B is 203. Than the probability that a randomly chosen subset of S is “nice” is :
(a) 7/2²⁰
(b) 5/2²⁰
(c) 4/2²⁰
(d) 6/2²⁰
Answer : B

Question. If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is :
(a) 1/21
(b) 1/27
(c) 1/15
(d) 1/26
Answer : B

Question. For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = 1/4 and P(All the three events occur simultaneously) = 1/16.
Then the probability that at least one of the events occurs, is :
(a) 3/16
(b) 7/32
(c) 7/16
(d) 764
Answer : C

Question. Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ...20}.
Statement -1: The probability that the chosen numbers when arranged in some order will form an AP is 1/85
Statement -2 : If the four chosen numbers form an AP, then the set of all possible values of common difference is (±1,±2,±3,±4,±5) .
(a) Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1
(b) Statement -1 is true, Statment -2 is false
(c) Statement -1 is false, Statment -2 is true.
(d) Statement -1 is true, Statement -2 is true ; Statement - 2 is a correct explanation for Statement -1.
Answer : B

Question. An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is
(a) 2/7
(b) 1/21
(c) 2/23
(d) 1/3
Answer : A

Question. From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :
(a) 21/220
(b) 3.11
(c) 1.11
(d) 2.23
Answer : C

Question. If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :
(a) 220(1/3)¹²
(b) 22(1/3)¹¹
(c) 55/3(2/3)¹¹
(d) 55(2/3)¹⁰
Answer : C

Question. A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P(A∪B) is
(a) 3/5
(b) 0
(c) 1
(d) 2/5
Answer : C

Question. A and B are events such that P(A ∪ B)=3/4, P(A ∩ B)=1/4, P(A) = 2/3 then P ( A ∩ B) is 
(a) 5/12
(b) 3/8
(c) 5/8
(d) 1/4
Answer : A

Q.1 A coin is tossed and a die is thrown. Find the probability that the outcome will be a head and a number greater than 4.

Q.2 In a class of 60 students, 32 like Maths, 30 like Biology and 24 like both Maths and Biology. If one of these students is selected at random, find the probability that the selected student.
(a) likes Maths or Biology
(b) likes neither Maths nor Biology
(c) likes Maths but not Biology.

Q.3 A fair coin with 1 marked on one face and 4 on the other and a fair die are both tossed, write the sample of the experiment.

Q.4 Give an example of a sure event and an impossible event.

Q.5 A box contains 10 red marbles, 20 blue marbles and 30 green marbles, 5 marbles are drawn from the box, what is the probability that (i) all will be blue? (ii) at least one will be green?

Q.6 A die is thrown, find the probability of the following events :
(i) A prime number will appear.
(ii) A number less than 6 will appear.
(iii) A number greater than or equal to 3 will appear.

Q.7 Three coins are tossed. Describe :
(i) two events which are mutually exclusive.
(ii) three events which are mutually exclusive and exhaustive.

Q.8 If 2/11 is the probability of an event, what is the probability of the event ‘not A’.

Q.9 Four cards are drawn at random from a pack of 52 playing cards. Find the probability of getting:
(a) all the four cards of the same suit.
(b) two red cards and two black cards. (
c) all cards of the same color. (d) one card from each suit.

Q.10 The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is probability of passing the Hindi examination

Q.11 Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment
A : ‘the sum is even’
B : ‘the sum is multiple of 3’
C : ‘the sum is less than 4’
D : ‘the sum is greater than 11’
Which pairs of these events are mutually exclusive?

Q.12 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be (i) a diamond (ii) not an ace.

Q.13 Three dice are thrown simultaneously. Find the probability that:
(a) all of them show the same face.
(b) all show different faces. (
c) two of them show the same face.

Q.14 A bag contains 5 white and 3 black balls. Four balls are successively drawn out without replacement. What is the probability that they are alternatively of different colours?

Q.15 Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10. The probability that both will qualify the examination is 0.02. Find the probability that (i) both Anil and Ashima will not qualify the examination (ii) at least one of them will not qualify the examination, and (iii) only one of them will qualify the examination.

Q.16 Tickets are numbered from 1 to 25. They are well shuffled and a ticket drawn at random . What is the probability that the drawn ticket has a prime number?

Q.17 The probability that a person visiting a doctor will have his blood test done is 0.75 and the probabilitythat he will be admitted is 0.30. The probability that he will have his blood test done or be admitted is 0.45. Find the probability that a person visiting the doctor will have his blood test done and be admitted? 

Q.18 Find the probability that in a random arrangement of the word ‘society’ all the three vowels come together. 

Q.19 In a lottery, a person choses six different natural numbers at random from 1 to 20, and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game? [Hint : Order of the numbers is not important]

Q.20 Find the probability that a leap year selected at random will contain 53 Mondays.