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

Answer 1

The correct option is D

$\frac{5}{4}$

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.

$\therefore$It is the binomial distribution.

Total number of times die thrown $=6$

$\mathrm{n}=6$

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 $\text{'}\mathrm{p}\text{'}=\frac{3}{6}$

$=\frac{1}{2}$

Probability of failure $\begin{array}{rcl}\text{'}\mathrm{q}\text{'}& =& 1-\frac{1}{2}\left[\because \mathrm{p}+\mathrm{q}=1\right]\end{array}$

$\begin{array}{rcl}& =& \frac{1}{2}\end{array}$

Step3. Calculate variance.

$\text{Variance = npq}$

Substitute the value of $\mathrm{n},\mathrm{p}\mathrm{and}\mathrm{q}$ in the formula

$\therefore \mathrm{Variance}=5\times \frac{1}{2}\times \frac{1}{2}$

$=\frac{\mathbf{5}}{\mathbf{4}}$

Hence, Option (D) is the correct answer.