Question

A die is thrown 100 times, getting an even number is considered a success. Variance of number of successe, is

• A. $10$
• B. $20$
• C. $25$
• D. $50$

Answer 1

The correct option is C $25$

This is an example of a binomial distribution.

Let $A$ be the event of obtaining an even number when a fair dice is thrown.

$\therefore p_A=\frac{1}{2}$

$\therefore p_{A^c}=1-p_A=\frac{1}{2}$

Variance over 100 trials = $n{p}_A{p}_{A^c}=100\times \frac{1}{4}=25$