A die is thrown 4 times and getting 3 is considered a success. The probability of 2 successes is:

$\frac{25}{216}$

The correct answer is Option (3) → $\frac{25}{216}$

$n=4,\;p=\frac{1}{6},\;q=\frac{5}{6}.$

$P(X=2)=\frac{4!}{2!(4-2)!}\left(\frac{1}{6}\right)^2\left(\frac{5}{6}\right)^2.$

$=\frac{4!}{2!2!}\cdot\frac{1}{36}\cdot\frac{25}{36}.$

$=6\cdot\frac{25}{1296}.$

$=\frac{150}{1296}.$

$=\frac{25}{216}.$

$P(X=2)=\frac{25}{216}.$