Q. If $X$ has binomial distribution with mean $np$ and variance $npq,\ then\frac{P(X = k)}{P(X = k - 1)}$ is equal to
A) $\frac{n - k}{k - 1}.\frac{p}{q}$
B) $\frac{n - k + 1}{k}.\frac{p}{q}$
C) $\frac{n + 1}{k}.\frac{q}{p}$
D) $\frac{n - 1}{k + 1}.\frac{q}{p}$
Explanation
(b)
$\frac{P(X = K)}{P(X = k - 1)} = \frac{\ ^{n}C_{k}p^{k}q^{n - k}}{\ ^{n}C_{k - 1}p^{k - 1}q^{n - k + 1}}$
$= \left( \frac{n - k + 1}{k} \right).\frac{p}{q}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.