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, $E=\{X$ is a prime number$\}$ and $F=X<4$, the probability $P(E\cup F)$ is

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

Answer 1

Answer: (B)

$0.77$

From the given values, prime numbers and the values less than $4$ are $1,2,3,5,7$
So, $P(E\cup F)$ will be the sum of probabilities of each of the above selected values of $X$
So, $P(E\cup F)=0.15+0.23+0.12+0.20+0.07=0.77$