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(A) Let $n = 5$ be the number of trials and $X$ be the number of times an even number appears.The probability of getting an even number in a single th

Vedclass · Accepted Answer

$5/16$

Vedclass · Answer

(A) Let $n = 5$ be the number of trials and $X$ be the number of times an even number appears.The probability of getting an even number in a single throw is $p = 3/6 = 1/2$.The probability of not getting an even number is $q = 1 - p = 1/2$.Using the binomial distribution formula $P(X = k) = \binom{n}{k} p^k q^{n-k}$,we need to find $P(X = 3)$:$P(X = 3) = \binom{5}{3} 	imes (1/2)^3 	imes (1/2)^{5-3}$$P(X = 3) = 10 	imes (1/8) 	imes (1/4)$$P(X = 3) = 10/32 = 5/16$.

What is the probability of getting an even number exactly $3$ times when a die is thrown $5$ times?

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