If a die is thrown 7 times,what is the probab | vedclass

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(D) This is a binomial distribution problem where $n = 7$ (number of trials),$k = 4$ (number of successes),$p = \frac{1}{6}$ (probability of getting a

Vedclass · Accepted Answer

$^7{C_4}{\left( {\frac{1}{6}} \right)^4}{\left( {\frac{5}{6}} \right)^3}$

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(D) This is a binomial distribution problem where $n = 7$ (number of trials),$k = 4$ (number of successes),$p = \frac{1}{6}$ (probability of getting a $5$ in a single throw),and $q = 1 - p = \frac{5}{6}$ (probability of not getting a $5$).Using the binomial probability formula $P(X = k) = ^n{C_k} \cdot p^k \cdot q^{n-k}$:$P(X = 4) = ^7{C_4} \cdot \left( \frac{1}{6} \right)^4 \cdot \left( \frac{5}{6} \right)^{7-4}$$P(X = 4) = ^7{C_4} \cdot \left( \frac{1}{6} \right)^4 \cdot \left( \frac{5}{6} \right)^3$Thus,the correct option is $D$.

If a die is thrown $7$ times,what is the probability of getting exactly $5$ four times?

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