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

View Answer

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

View Answer

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 x_{1}, x_{2}, x_{3} 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

View Answer

Explanation: We know that ∑P(x

_{i}) = 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

View Answer

Explanation: We know that ∑P(x

_{i})=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

View Answer

Explanation: We know that ∑P(x

_{i})=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

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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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