JEE Mains · Maths · STD 12 - 13. probability
The random valuable \(X\) follows binomial distribution \(B (n, p)\) for which the difference of the mean and the variance is \(1\). If \(2 P(X=2)=3 P(X=1)\), then \(n^2 P(X > 1)\) is equal to \(......\).
- A \(12\)
- B \(15\)
- C \(11\)
- D \(16\)
Answer & Solution
Correct Answer
(C) \(11\)
Step-by-step Solution
Detailed explanation
\(n p-n p q=1\) \(\Rightarrow np ^2=1\) \(2^{ n } C _2 p ^2 q ^{ n-2 }=3^{ n } C _1 p q^{n-1}\) \(\Rightarrow n p-p=3 q \quad(\therefore q=1-p)\) \(\Rightarrow p =\frac{1}{2}\) Hence \(n=4\) \(P(x > 1)=1-(p(x=0)+p(x=1)\)…
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