Question

A random variable $X$ has the probability distribution
For the events $E=\left\{xisprimenumber\right\}$ and $F=\{x<4\}$ the probability of $P(E\cup F)$ is

• A. $0.50$
• B. $0.77$
• C. $0.35$
• D. $0.87$

Answer 1

The correct option is B $0.77$

Given, $E=\left\{xisaprimenumber\right\}$
$P\left(E\right)=P\left(2\right)+P\left(3\right)+P\left(5\right)+P\left(7\right)$
$=0.23+0.12+0.20+0.07=0.62$
and $F=\{x<4\}$
$P\left(F\right)=P\left(1\right)+P\left(2\right)+P\left(3\right)$
$=0.15+0.23+0.12=0.50$
and $P(E\cap F)=P\left(2\right)+P\left(3\right)$
$=0.23+0.12=0.35$
$\therefore P(E\cup F)=P\left(E\right)+P\left(F\right)-P(E\cap F)$
$=0.62+0.50-0.35$
$=0.77$