Suppose $E$ and $F$ are two events of a random experiment. If the probability of occurrence of $E$ is $1 /…
Suppose $E$ and $F$ are two events of a random experiment. If the probability of occurrence of $E$ is $1 / 5$ and the probability of occurrence of $F$ given $E$ is $1 / 10$, then the probability of non-occurrence of atleast one of the events $E$ and $F$ is
$\frac{1}{18}$
$\frac{1}{2}$
$\frac{49}{50}$
$\frac{1}{50}$
Solution
Given that,
$
P(E)=\frac{1}{5}, P(F)=\frac{1}{10}
$
Probability of both occurrence,
$
P(E \cap F)=P(E) P(F)
$
$
=\frac{1}{5} \cdot \frac{1}{10}=\frac{1}{50}
$
Required Probability $=1-P(E \cap F)$
$
=1-\frac{1}{50}=\frac{49}{50}
$