If in a binomial distribution n=4,P(X=0)=16 81 , then P(X=4) equa… - Vidyadip

Question

If in a binomial distribution $\text{n}=4,\text{P(X}=0)=\frac{16}{81},$ then $\text{P(X}=4)$ equals:

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Answer

$\frac{1}{81}$

Solution:
Given $\text{n}=4,\text{P(X}=0)=\frac{16}{81}$
$\text{P(X}=0)=\frac{16}{81}$
$\text{ }^5\text{C}_0\text{p}^0\text{q}^4=\frac{16}{81}$
$\text{q}^4=\frac{16}{81}$
$\text{q}=\frac{2}{3}\Rightarrow\text{p}=\frac{1}{3}$
$\Rightarrow\text{P(X}=4)=\text{ }^5\text{C}_4\big(\frac{1}{4}\big)^4=\frac{1}{81}$

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