A fair die is thrown 4 times. If getting a pr | vedclass

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(A) $1$. The sample space of a fair die is $S = \{1, 2, 3, 4, 5, 6\}$, so the total outcomes $n(S) = 6$.$2$. Prime numbers on a die are $\{2, 3, 5\}$,

Vedclass · Accepted Answer

$1/16$

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(A) $1$. The sample space of a fair die is $S = \{1, 2, 3, 4, 5, 6\}$, so the total outcomes $n(S) = 6$.$2$. Prime numbers on a die are $\{2, 3, 5\}$, so the number of successful outcomes is $3$.$3$. Probability of success in a single throw, $p = 3/6 = 1/2$.$4$. Probability of failure in a single throw, $q = 1 - p = 1 - 1/2 = 1/2$.$5$. The die is thrown $n = 4$ times. The probability of getting no success (i.e., $0$ successes) is given by the binomial distribution formula $P(X = k) = \binom{n}{k} p^k q^{n-k}$.$6$. For $k = 0$, $P(X = 0) = \binom{4}{0} (1/2)^0 (1/2)^{4-0} = 1 	imes 1 	imes (1/2)^4 = 1/16$.

$A$ fair die is thrown $4$ times. If getting a prime number on the die is considered as a success, then the probability of getting no success at all is ...

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