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In a 5-trial binomial distribution, $P(X = 1) = 0.4096$ and $P(X = 2) = 0.2048$. The probability of success $p$ is:
A$0.1$
B$0.2$
C$0.4$
D$0.5$
Answer & Solution
Correct answer: B. $0.2$
$P(2)/P(1) = ({}^5C_2 p^2 q^3) / ({}^5C_1 p q^4) = (10/5)(p/q) = 2p/q$. Given ratio = $0.2048/0.4096 = 0.5$. So $2p/q = 0.5$ ⇒ $4p = q = 1 - p$ ⇒ $p = 1/5 = 0.2$.
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