Probability
Binomial with Equal Probabilities — Finding n
nta_pyq_2023_apr
Grade 12
Question:
A die is rolled $n$ times. $P(\text{odd 7 times})=P(\text{odd 9 times})$. If $P(\text{even twice})=\dfrac{k}{2^{15}}$, then $k$ is equal to
Step-by-Step Solution
Key Concept: $p=q=\frac{1}{2}$. $\binom{n}{7}=\binom{n}{9}\Rightarrow n=16$. $P(\text{even twice})=\binom{16}{2}(\frac{1}{2})^{16}=\frac{120}{2^{16}}=\frac{60}{2^{15}}$.
$n=16$, $k=60$.
Correct Answer: 1