Q. Suppose $E$ and $F$ are two independent events of a random experiment. If the probability of occurrence of $E$ is$\frac{1}{5}$and the probability of occurrence of $F$ given $E$ is $\frac{1}{10}$,then the probability of non-occurrence of at least one of the events $E$ and $F$ is
A) $\frac{1}{18}$
B) $\frac{1}{2}$
C) $\frac{49}{50}$
D) $\frac{1}{50}$
Explanation
(c)
Probability of both occurrence,
$P(E \cap F) = P(E)P(F)$
$= \frac{1}{5}.\frac{1}{10} = \frac{1}{50}$
Required probability $= 1 - P(E \cap F)$
$= 1 - \frac{1}{50} = \frac{49}{50}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.