Let a die be rolled n times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd number nine times. If the probability of getting even number twice is $\frac{\mathrm{k}}{2^{15}},$ then k is equal to 

$$\begin{gathered} \text{ Probability of getting odd }=\frac{1}{2}\text{ Probability of getting even }=\frac{1}{2} \\ \text{ probability of getting odd numbers seven times }=\left(\begin{array}{l}\mathrm{n}\\ 7\end{array}\right){\left(\frac{1}{2}\right)}^{\mathrm{n}} \\ \text{ probability of getting odd number nine times }=\left(\begin{array}{l}\mathrm{n}\\ 9\end{array}\right){\left(\frac{1}{2}\right)}^{\mathrm{n}} \\ \text{ Given }\left(\begin{array}{l}\mathrm{n}\\ 7\end{array}\right){\left(\frac{1}{2}\right)}^{\mathrm{n}}=\left(\begin{array}{l}\mathrm{n}\\ 9\end{array}\right){\left(\frac{1}{2}\right)}^{\mathrm{n}}\Rightarrow \mathrm{n}=7+9=16 \\ \text{ probability of getting even number twice }\left(\begin{array}{c}16\\ 2\end{array}\right){\left(\frac{1}{2}\right)}^{16}=\frac{16\times 15}{2}{\left(\frac{1}{2}\right)}^{16}=\frac{60}{2^{15}} \end{gathered}$$