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(B) Given that $X$ is a binomial variate with $n=6$ and probability of success $p$. Let $q = 1-p$ be the probability of failure.The probability mass f

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$1/3$

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(B) Given that $X$ is a binomial variate with $n=6$ and probability of success $p$. Let $q = 1-p$ be the probability of failure.The probability mass function is given by $P(X=r) = {}^{n}C_{r} p^{r} q^{n-r}$.We are given the condition $4 P(X=4) = P(X=2)$.Substituting the formula:$4 \cdot {}^{6}C_{4} p^{4} q^{6-4} = {}^{6}C_{2} p^{2} q^{6-2}$$4 \cdot {}^{6}C_{4} p^{4} q^{2} = {}^{6}C_{2} p^{2} q^{4}$Since ${}^{6}C_{4} = {}^{6}C_{2} = 15$, we can cancel them:$4 p^{4} q^{2} = p^{2} q^{4}$Dividing both sides by $p^{2} q^{2}$ (assuming $p, q 
eq 0$):$4 p^{2} = q^{2}$Taking the square root of both sides:$2p = q$Since $q = 1-p$, we have:$2p = 1-p$$3p = 1$$p = 1/3$

Let $X$ be a binomial variate with parameters $n=6$ and $p$. If $4 P(X=4)=P(X=2)$, then $p$ equals

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