A pair of dice is thrown 4 times. If 'getting a doublet' is considered a success, find the probability of getting 2 successes.

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A pair of dice is thrown 4 times. If ‘getting a doublet’ is considered a success, find the probability of getting 2 successes.

A pair of dice is thrown 4 times. If ‘getting a doublet’ is considered a success, find the probability of getting 2 successes.

As the pair of die is thrown 4 times,
The total number of outcomes $=36$
Using Bernoulli’s Trial $P($ Success $=x)={ }^{n} C_{x} \cdot p^{x} \cdot q^{(n-x)}$
$x=0,1,2, \ldots \ldots . . n$ and $q=(1-p)$
The probability of success $=p=\frac{6}{36}=\frac{1}{6}$
$q=\frac{5}{6}$
probability of 2 successes $={ }^{4} C_{2} \cdot\left(\frac{1}{6}\right)^{2}\left(\frac{5}{6}\right)^{2}$
$\Rightarrow \frac{25}{216}$