JEE PYQ: Probability Question 38
Question 38 - 2019 (12 Apr Shift 1)
Let a random variable $X$ have a binomial distribution with mean 8 and variance 4. If $P(X \leq 2) = \frac{k}{2^{16}}$, then $k$ is equal to:
(1) 17
(2) 121
(3) 1
(4) 137
Show Answer
Answer: (4)
Solution
$np = 8$, $npq = 4 \Rightarrow q = \frac{1}{2}$, $p = \frac{1}{2}$, $n = 16$. $P(X \leq 2) = \frac{{}^{16}C_0 + {}^{16}C_1 + {}^{16}C_2}{2^{16}} = \frac{1 + 16 + 120}{2^{16}} = \frac{137}{2^{16}}$. So $k = 137$.
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