Question

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

• A. $\frac{8}{3}$
• B. $\frac{3}{8}$
• C. $\frac{4}{5}$
• D. $\frac{5}{4}$

Answer 1

Answer: (D)

$\frac{5}{4}$

The probability of getting an odd number is $\frac{3}{6}=\frac{1}{2}$

In the given distribution. the number of success are in a sequence of n independent experiments each asking yes-no i.e., whether the outcome is even or odd. Therefore, the given distribution is binomial distribution.

The variance for the binomial distribution is $npq$

where $p$ is the success probability

$q$ is the failure probability

$n$ is the number of experiments.

$p=\frac{1}{2}$ and

$q=1-p=1-\frac{1}{2}=\frac{1}{2}$

Given that the number of experiments is $n=5$

Therefore, variance is $npq=5\ast \frac{1}{2}\ast \frac{1}{2}=\frac{5}{4}$