Question

A random variable $X$ has the probability distribution:

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

For the events $E=\left\{x|x\text{is prime}\right\}$ and $F=\{x|x<4\}$, the probability $P(E\cup F)$ is

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

Answer 1

Answer: (B)

$0.77$

Using given table, $P\left(E\right)=0.62,P\left(F\right)=0.5,P(E\cap F)=0.35$.
$\therefore P(E\cup F)=P\left(E\right)+P\left(F\right)-P(E\cap F)=0.62+0.5-0.35=.77$