JEE PYQ: Probability Question 13
Question 13 - 2021 (26 Feb Shift 1)
A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is:
(1) $\frac{15}{2^{12}}$
(2) $\frac{15}{2^{13}}$
(3) $\frac{15}{2^{14}}$
(4) $\frac{15}{2^8}$
Show Answer
Answer: (2)
Solution
${}^nC_7 \left(\frac{1}{2}\right)^n = {}^nC_9 \left(\frac{1}{2}\right)^n \Rightarrow {}^nC_7 = {}^nC_9 \Rightarrow n = 16$. $P(X=2) = {}^{16}C_2 \left(\frac{1}{2}\right)^{16} = \frac{120}{2^{16}} = \frac{15}{2^{13}}$.
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