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  4. If x follows the Binomial distribution with parameters n = 6 and p and 9P (X = 4) = P(X = 2) , then p is

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Q. If $ x $ follows the Binomial distribution with parameters $ n = 6 $ and $ p $ and $ 9P (X = 4) $ $ = P(X = 2) $ , then $ p $ is

MHT CETMHT CET 2011

Solution:

Given, 9P $(X=4)=P(X=2)$
$\therefore 9 \cdot{ }^{6} C_{4} p^{4}(1-p)^{2}={ }^{6} C_{2} p^{2}(1-p)^{4}$
$\Rightarrow \frac{(1-p)^{2}}{p^{2}}=9$
$\Rightarrow \frac{1-p}{p}=3$
$\Rightarrow p=1 / 4$