Question

A random variable $X$ has the probability distribution:

$X$:	1	2	3	4	5	6	7	8
$p\left(X\right)$:	0.2	0.2	0.1	0.1	0.2	0.1	0.1	0.1

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

• A. $0.50$
• B. $0.77$
• C. $0.35$
• D. $0.80$

Answer 1

The correct option is D $0.80$

given I = $\{$'x' is a prime number $\}$

P(E) = p(x=2 or x = 3 or x =5 or x =7)

$=P(x=2)+p(x=3)+p(x=5)+p(x=7)$

$=0.2+0.1+0.2+0.1$

$p\left(B\right)=0.6$

$p\left(F\right)=P(x=1)+p(x=2)+p(x=3)$

$=0.2+0.2+0.1$

$=0.5$

$p\left(EAF\right)=p(x=2)+p(x=3)$

$=0.2+0.1$

$0.3$

$p(E\vee F)=p\left(E\right)+p\left(F\right)-p(E\wedge F)$

$=0.6+0.5=0.3$

$P(E\vee F)=0.80$