A fair coin is tossed a fixed number of times . If the probability of getting 7 heads is equal to getting 9 heads, then the probability of getting 2 heads is,
Answer & explanation
Correct answer: option 3
Let coin was tossed 'n' times and X be the random variable representing the number of head appearing in 'n' trials.
$P(X=7)=P(X=9) \Rightarrow{ }^n C_7(1 / 2)^7(1 / 2)^{n-7}={ }^n C_9(1 / 2)^{n-9} \times(1 / 2)^9$
$\Rightarrow{ }^n C_7={ }^n C_9 \Rightarrow n=16$
Now $P(X=2)={ }^{16} C_2(1 / 2)^2(1 / 2)^{14}=\frac{{ }^{16} C_2}{2^{16}}=\frac{16.15}{2^{17}}=\frac{15}{2^{13}}$