Let a die be rolled n times.

Question

Let a die be rolled $n$ times. If $P(	ext{odd 7 times})=P(	ext{odd 9 times})$, and $P(	ext{even twice})=\dfrac{k}{2^{15}}$, find $k$.

Accepted Answer

${}^nC_7={}^nC_9 \Rightarrow n=16$.

$$P(\text{even twice}) = {}^{16}C_2\left(\frac12\right)^{16} = \frac{120}{2^{16}}=\frac{60}{2^{15}} \implies k=60$$

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