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A Die is Tossed Twice. a 'Success' is Getting an Even Number on a Toss. Find the Variance of Number of Successes. - Mathematics

Question

A die is tossed twice. A 'success' is getting an even number on a toss. Find the variance of number of successes.

Solution

$\text{ We have,}$
$p =\text{ probability of getting an even number on a toss } = \frac{3}{6} = \frac{1}{2} and$
$q = 1 - p = 1 - \frac{1}{2} = \frac{1}{2}$
$\text{ Let X denote a success of getting an even number on a toss . Then, }$
$\text{ X follows binomial distribution with parameters n = 2 and } p = \frac{1}{2}$
$\therefore Var\left( X \right) = \text{ npq } = 2 \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{2}$

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