A die is thrown 100 times. If the success is | vedclass

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(B) Let $X$ be the number of successes in $n = 100$ trials. This follows a binomial distribution $B(n, p)$.Here,the probability of getting an even num

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$25$

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(B) Let $X$ be the number of successes in $n = 100$ trials. This follows a binomial distribution $B(n, p)$.Here,the probability of getting an even number in a single throw of a die is $p = \frac{3}{6} = \frac{1}{2}$.The probability of failure is $q = 1 - p = 1 - \frac{1}{2} = \frac{1}{2}$.The variance of a binomial distribution is given by the formula $	ext{Var}(X) = npq$.Substituting the values,we get $	ext{Var}(X) = 100 	imes \frac{1}{2} 	imes \frac{1}{2} = 100 	imes \frac{1}{4} = 25$.Therefore,the variance is $25$.

$A$ die is thrown $100$ times. If the success is defined as getting an even number,then the variance of the number of successes is:

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