# Mathematics Questions and Answers – Random Variables and its Probability Distributions

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This set of Mathematics Online Quiz for Class 12 focuses on “Random Variables and its Probability Distributions”.

1. A month has atmost 31days, X = Number of days in a month, is X a discrete random variable?
a) True
b) False

Explanation: X = Number of days in a month.
The number of days in a month can be 29,30,31
X takes finite values so, therefore it is Discrete and range X = {28,29,30,31}

2. Find which of the following is a Continuous random variable?
a) Number of kids in a family
b) Number of planets around the sun
c) Number of tails tossing a coin four times
d) Life of an electric fan

Explanation: Except life of an electric fan, remaining all takes finite values. Life of an electric fan takes infinite values so it is a continuous random variable.

3. Find the value of P(X=3) if X is the discrete random variable taking values x1, x2, x3 where P(X=0)=0, P(X=1) = 1/4 and P(X=2) = 1/4
a) 1
b) 1/2
c) 1/3
d) 1/4

Explanation: We know that ∑P(xi) = 1
P(X) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
1 = 1/4 + 1/4 + P(X=3)
P(X=3) = $$\frac {1}{2}$$

4. Let X be the random variable , P(X=x) is the Probability mass function is given by

 X 0 1 2 3 P(X=x) 0 k 2k 3k

Determine the value of K?
a) 1/5
b) 2/5
c) 1/6
d) 1/2

Explanation: We know that ∑P(xi)=1
P(X) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
1 = 0 + k + 2k + 3k
1 = 6k
K = 1/6

5. Let X be the random a variable, P(X=x) is the Probability mass function is given by

 X 0 1 2 3 P(X=x) 0 1/2 2k 3k

Determine the value of k?
a) 1/8
b) 1/4
c) 1/6
d) 1/2

Explanation: We know that ∑P(xi)=1
P(X) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
1 = 0 + 1/2 + 2k + 2k
1/2 = 4k
k = 1/8

6. Determine the value c so that the following function can serve as a probability distribution of the discrete random variable x:
f(x)=c(x+4), for x=0,1,2,3
a) 1/20
b) 1/16
c) 1/18
d) 1/22

Explanation: f(x)=c(x+4), for x=0,1,2,3
c(0+4) + c(1+4) + c(2+4) + c(3+4) = 1
4c + 5c + 6c + 7c = 1
22c = 1
c = 1/22

7. A dice is thrown, what is the probability of getting an odd number?
a) 1/8
b) 1/6
c) 1/2
d) 1/4

Explanation: Possible outcomes when a dice is thrown = {1,2,3,4,5,6}$$\frac {number \, of \, odd \, numbers}{number \, of \, possible \, outcomes} = \frac {3}{6}=\frac {1}{2}$$

8. Let X be the random variable, P(X=x) is the Probability mass function is given by

 X 0 1 2 3 P(X=x) 1/8 1/2 1/8 1/4

Find the value of P(X ≥ 1)
a) 5/7
b) 7/8
c) 3/8
d) 8/9

Explanation: P(X ≥ 1) = P(X=1) + P(X=2) + P(X=3)
= 1/2 + 1/8 + 1/4
= 7/8

9. Let X be the random variable, P(X=x) is the Probability mass function is given by

 X 0 1 2 3 4 P(X=x) 1/8 1/2 1/16 1/4 1/16

Find the value of F(1)
a) 1/5
b) 8/5
c) 2/5
d) 5/8

Explanation: F(1)=P(X ≤ 1)
P(X ≤ 1) = P(X=1) + P(X=0)
= 1/2 + 1/8
= 5/8

10. Let X be the random variable, P(X=x) is the Probability mass function is given by

 X 0 1 2 3 4 P(X=x) 1/11 3/11 2/11 4/11 1/11

Find the value of F(4)
a) 9/11
b) 1
c) 5/11
d) 1/2

Explanation: F(4)=P(X ≤ 4)
P(X ≤ 4) = P(X=4) + P(X=3) + P (X=2) + P(X=1) + P(X=0)
= 1/11 + 4/11 + 2/11 + 3/11 + 1/11
= 1

11. A dice is thrown, what is the probability of getting an even number?
a) 1/8
b) 1/6
c) 1/2
d) 1/4

Explanation: Possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6}
$$\frac {number \, of \, even \, numbers}{number \, of \, possible \, outcomes} = \frac {3}{6}=\frac {1}{2}$$

12. A dice is thrown, what is the probability of getting multiples of 3?
a) 1/8
b) 1/6
c) 1/2
d) 1/3

Explanation: Possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6}
Multiples of 3 = {3, 6}
Total probability = $$\frac {number \, of \, multiples \, of \, 3}{number \, of \, possible \, outcomes} = \frac {2}{6}=\frac {1}{3}$$

13. A dice is thrown, what is the probability of getting multiples of 2?
a) 1/8
b) 1/6
c) 1/2
d) 1/3

Explanation: Possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6}
Multiples of 2 = {2, 4, 6}
Total probability = $$\frac {number \, of \, multiples \, of \, 3}{number \, of \, possible \, outcomes} = \frac {3}{6}=\frac {1}{2}$$

14. What is the probability of picking an ace from a pack of cards?
a) 1/8
b) 1/6
c) 1/2
d) 1/13

Explanation: Total number cards in a pack = 52
Total number of aces in a pack of cards = 4
Total probability = $$\frac {number \, of \, aces}{number \, of \, cards \, in \, a \, pack}= \frac {4}{52}=\frac {1}{13}$$

15. What is the probability of picking a card of the club from a pack of cards?
a) 1/8
b) 1/4
c) 1/2
d) 1/13

Explanation: Total number cards in a pack = 52
Total number of clubs in a pack of cards = 4
Total probability = $$\frac {number \, of \, clubs}{number \, of \, cards \, in \, a \, pack} = \frac {13}{52}$$

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