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Question
If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9, P(X = 3), then p = ______.
Solution
If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9, P(X = 3), then p = `1/10`.
Explanation:
Given that: P(X = 2) = 9P(X = 3)
⇒ `""^5"C"_2 "p"^2 "q"^3` = 9. `""^5"C"_3 "p"^3 "q"^2`
⇒ `1/9 = (""^5"C"_3 "p"^2 "q"^2)/(""^5"C"_2 "p"^2 "q"^3)`
⇒ `1/9 = "p"/"q"` .......`[because ""^5"C"_3 = ""^5"C"_2]`
⇒ 9p = q
⇒ 9p = 1 – p
⇒ 9p + p = 1
⇒ 10p = 1
∴ p = `1/10`
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