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If $x$ follows the Binomial distribution with parameters $n=6$ and $p$ and $9 P(X=4)$ $=P(X=2)$, then $p$ is
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The correct answer is:
$1 / 4$
Given, $9 P(X=4)=P(X=2)$
$\therefore \quad 9 \cdot{ }^{6} C_{4} p^{4}(1-p)^{2}={ }^{6} C_{2} p^{2}(1-p)^{4}$
$\Rightarrow \quad \frac{(1-p)^{2}}{p^{2}}=9$
$\Rightarrow \quad \frac{1-p}{p}=3$
$\Rightarrow \quad p=1 / 4$
$\therefore \quad 9 \cdot{ }^{6} C_{4} p^{4}(1-p)^{2}={ }^{6} C_{2} p^{2}(1-p)^{4}$
$\Rightarrow \quad \frac{(1-p)^{2}}{p^{2}}=9$
$\Rightarrow \quad \frac{1-p}{p}=3$
$\Rightarrow \quad p=1 / 4$
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