Question

A random variable $X$ has the probability distribution :

$X$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P\left(X\right)$	$0.15$	$0.23$	$0.12$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

For the events $E=\left\{Xisaprimenumber\right\}$ and $F=\{X<4\}$, then what is the probability $P(E\cup F)?$

Answer 1

$E=\left\{Xisaprimenumber\right\}$

$P\left(E\right)=P\left(2\right)+P\left(3\right)+P\left(5\right)+P\left(7\right)=0.23+0.12+0.20+0.07=0.42$

$F=\{x<4\}$

$P\left(F\right)=P\left(1\right)+P\left(2\right)+P\left(3\right)=0.15+0.23+0.12=0.50$

and $P(E\cap F)=P\left(2\right)+P\left(3\right)=0.35$

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