Let X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p). What is the conditional probability P(X≥1∣X≤1)P(X \ge 1 \mid X \le 1)P(X≥1∣X≤1)?
np1+(n−1)p\frac{n p}{1 + (n-1)p}1+(n−1)pnp
np1−p\frac{np}{1-p}1−pnp
npnpnp
p1+(n−1)p\frac{p}{1 + (n-1)p}1+(n−1)pp