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.
Answer & explanation
Correct answer: option 4
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 = $P(2) = {^5C}_2p^2q^3$
$= 10(0.2)^2 (0.8)^3 = 0.2048$