A die is thrown 4 times and getting 3 is considered a success. The probability of 2 successes is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{25}{216}$
$n=4,\;p=\frac{1}{6},\;q=\frac{5}{6}.$
$P(X=2)=\frac{4!}{2!(4-2)!}\left(\frac{1}{6}\right)^2\left(\frac{5}{6}\right)^2.$
$=\frac{4!}{2!2!}\cdot\frac{1}{36}\cdot\frac{25}{36}.$
$=6\cdot\frac{25}{1296}.$
$=\frac{150}{1296}.$
$=\frac{25}{216}.$
$P(X=2)=\frac{25}{216}.$