Suppose a random variable X follows the binomial distribution with parameters n and p, where `0

Options

A. `1/2`
B. `1/3`
C. `1/5`
D. `1/7`

Explanation

To solve the problem, we need to find the value of \( p \) such that the ratio \( \frac{P(X = r)}{P(X = n - r)} \) is independent of \( n \) and \( r \).

### Step-by-Step Solution:

1. **Understand the Probability Mass Function**:
The probability of a binomial random variable \( X \) taking the value \( r \) is given by:
\[
P(X = r) = \binom{n}{r} p^r (1-p)^{n-r}
...