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Question

A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of the distribution of success is


A

83

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B

38

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C

45

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D

54

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Solution

The correct option is D

54


Explanation for the correct answer

Step1. Determine the type of distribution.

As die is thrown repeated a number of times, it is Bernoulli's trial.

It is the binomial distribution.

Total number of times die thrown =6

n=6

Probability of getting an odd number = Probability of success

Probability of getting an even number = Probability of failure

Step2. Calculate the Probability of success and failure.

Probability of success 'p'=36

=12

Probability of failure 'q'=1-12p+q=1

=12

Step3. Calculate variance.

Variance=npq

Substitute the value of n,pandq in the formula

Variance=5×12×12

=54

Hence, Option (D) is the correct answer.


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