A fair coin is tossed a fixed number of times. If the probability...

$P\left(H\right) = P\left(T\right) = \dfrac{1}{2}$

$P$($7$ heads)$= C7 n {\left(\dfrac{1}{2}\right)}^{n - 7}{\left(\dfrac{1}{2}\right)}^{7} = \dfrac{C7 n}{{2}^{n}}$

$P$($9$ heads)$= C9 n {\left(\dfrac{1}{2}\right)}^{n - 9}{\left(\dfrac{1}{2}\right)}^{9} = \dfrac{C9 n}{{2}^{n}}$

$P$($7$ heads)$= P$ ($7$heads)

$C7 n = C9 n ⇒ n = 16$

$P$($2$ heads)$= C2 16 {\left(\dfrac{1}{2}\right)}^{14}{\left(\dfrac{1}{2}\right)}^{2} = \dfrac{15 \times 8}{{2}^{16}}$

$P$($2$ heads)$= \dfrac{15}{{2}^{13}}$