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

$\frac{15}{2^{13}}$

Let the coin be tossed 'n' times and let X be the random variable representing the number of heads appearing in 'n' trials.

$P(X = 7) = P (X = 9) ⇒ {^n C}_7(1/2)^7 (1/2)^{n-7} = {^nC}_9(1/2)^{n-9} × (1/2)^9$

$⇒ {^nC}_7 = {^nC}_9 ⇒ n = 16$.

Now, $P (X = 2) = {^{16}C}_2(1/2)^2 (1/2)^{14} =\frac{{^{16}C}_2}{2^{16}}=\frac{16.15}{2^{17}} = \frac{15}{2^{13}}$.