JEE Mains · Maths · STD 12 - 13. probability
Let a random variable \(X\) have a binomial distribution with mean \(8\) and variance \(4\). If \(P\left( {X \le 2} \right) = \frac{k}{{{2^{16}}}}\), then \(k\) is equal to
- A \(17\)
- B \(137\)
- C \(1\)
- D \(121\)
Answer & Solution
Correct Answer
(B) \(137\)
Step-by-step Solution
Detailed explanation
\(\mathrm{np}=8\) \(\mathrm{npq}=4\) \(\mathrm{q}=\frac{1}{2} \Rightarrow \mathrm{p}=\frac{1}{2}\) \(n=16\) \(p(x=r)=^{16} C_{r}\left(\frac{1}{2}\right)^{16}\) \(p(x \leq 2)=\frac{^{16} C_{0}+^{16} C_{1}+^{16} C_{2}}{2^{16}}\) \(=\frac{137}{2^{16}}\)
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