A random variable $X$ has the probability distribution: $ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline…

A random variable $X$ has the probability distribution: $ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \mathrm{X}: & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \mathrm{p}(\mathrm{X}): & 0.15 & 0.23 & 0.12 & 0.10 & 0.20 & 0.08 & 0.07 & 0.05 \\ \hline \end{array}$ For the events $E=\{X$ is a prime number $\}$ and $F=\{X < 4\}$, the probability $P(E \cup F)$ is
  1. $0.87$
  2. $0.77$
  3. $0.35$
  4. $0.50$

Solution

$P(E \cup F)=P(E)+P(F)-P(E \cap F)=0.62+0.50-0.35=0.77$

Asked in: JEE Main 2004

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