If $^{'} X^{'}$ has a binomoial distribution with parameters $n = 6, p$ and $P (X = 2) = 12, P (X = 3) = 5$ then $p =$

\frac{1}{2}

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\frac{5}{12}

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\frac{5}{16}

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\frac{5}{21}

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Solution

The correct option is D $\frac{5}{21}$
$P (X = 2) = 12 \Rightarrow^{6} C_{2} (p)^{2} (1 - p)^{4} = 12 . . . . [1]$

$P (X = 3) = 5 \Rightarrow^{6} C_{3} (p)^{3} (1 - p)^{3} = 5 . . . . [2]$

Dividing $[1]$ by $[2]$ , we get

$\frac{15 (1 - p)}{20 p} = \frac{12}{5} \Rightarrow p = \frac{5}{21}$

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