If X B(6, p) and 2P(X = 3) = P(X = 2), then find p - Vidyadip

Question

If $X \sim B(6, p)$ and $2P(X = 3) = P(X = 2),$ then find $p$

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Answer

Given that $X \sim B(6, p)$
$\therefore n =6$
Also, it is given that $2 P(X=3)=P(X=2)$
$ \therefore 2 \times{ }^6 C_3 p^3 q^3={ }^6 C_2 p^2 q^4$
$\therefore 2 \times 20 \times p=15 \times q$
$\therefore 8 \times p=3(1-p)$
$\therefore 8 p=3-3 p$
$\therefore 11 p=3$
$\therefore p=\frac{3}{11} $

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