VBQs Probability Class 11 Mathematics with solutions has been provided below for standard students. We have provided chapter wise VBQ for Class 11 Mathematics with solutions. The following Probability Class 11 Mathematics value based questions with answers will come in your exams. Students should understand the concepts and learn the solved cased based VBQs provided below. This will help you to get better marks in class 11 examinations.

**Probability VBQs Class 11 Mathematics**

**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. If the events A and B are mutually exclusive events such that P(A) = (3x+1)/3 and P(B) = (1 – x)/4, then the set of possible values of x lies in the interval :**

(a) [0, 1]

(b) [1/3, 2/3]

(c) [- 1/3, 5/9]

(d) [- 7/9, 4/9]

## Answer

B

**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, Statement -2 is false

(c) Statement -1 is false, Statement -2 is true.

(d) Statement -1 is true, Statement -2 is true ; Statement – 2 is a correct explanation for Statement -1.

## Answer

B

**Question. Events A, B, C are mutually exclusive events such that**

**The set of possible values of x are in the interval.**

(a) [0 , 1]

(b) [1/3, 1/2]

(c) [1/3, 2/3]

(d) [1/3, 13/3]

## Answer

B

**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. 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. 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) 7/64

## 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 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. 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. 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 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. 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. 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) 965/2^{11}

(b) 965/2^{10}

(c) 945/2^{10}

(d) 945/2^{11}

## Answer

None

**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 x ∈ A is:**

(a) 1/2

(b) 64/127

(c) 63/128

(d) 31/128

## Answer

B

**Question. A box ‘A’ contains 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 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) 7/2^{20}

(b) 5/2^{20}

(c) 4/2^{20}

(d) 6/2^{20}

## Answer

B

**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. 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 and B are events such that P(A ∪ B) = 3/4, P(A ∩ B) = 1/4, P( A̅ ) = 2/3 then P ( A̅ ∩ B) is**

(a) 5/12

(b) 3/8

(c) 5/8

(d) 1/4

## 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

C

**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. 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. 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

C

**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. A number n is randomly selected from the set {1, 2, 3, ….. , 1000}. The probability that **

**is an integer is**

(a) 0.331

(b) 0.333

(c) 0.334

(d) 0.332

## Answer

C