If a dice is thrown 7 times,then the probabil | vedclass

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Question

(A) This is a problem of binomial distribution where the probability of success $p$ (getting a $5$) is $\frac{1}{6}$ and the probability of failure $q

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) This is a problem of binomial distribution where the probability of success $p$ (getting a $5$) is $\frac{1}{6}$ and the probability of failure $q$ (not getting a $5$) is $1 - \frac{1}{6} = \frac{5}{6}$.Here,the number of trials $n = 7$ and the number of successes required $r = 4$.The formula for binomial probability is $P(X = r) = {}^nC_r \cdot p^r \cdot q^{n-r}$.Substituting the values,we get $P(X = 4) = {}^7C_4 \left( \frac{1}{6} \right)^4 \left( \frac{5}{6} \right)^{7-4}$.Thus,the required probability is $^7C_4 \left( \frac{1}{6} \right)^4 \left( \frac{5}{6} \right)^3$.

If a dice is thrown $7$ times,then the probability of obtaining $5$ exactly $4$ times is

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