In a binomial distribution, the sum of its mean and variance is 1.8. Find the probability of two successes if the event was conducted 5 times.

0.2048

The correct answer is Option (4) → 0.2048

Here $np + npq = 1.8$ and $n = 5$

$⇒ 5p (1+ q) = 1.8⇒ (1-q)(1 + q) = 0.36 ⇒ 1-q^2 = 0.36$

$⇒ q^2 = 0.64⇒q=0.8$   $∵(0≤q≤1)$

$∴p = 0.2, q=0.8$ and $n = 5$.

∴ Probability of 2 successes = $P(2) = {^5C}_2p^2q^3$

$= 10(0.2)^2 (0.8)^3 = 0.2048$