Question

A random variable X has the probability distribution

$X=x_i$ :	1	2	3	4	5	6
$P(X=x_i)$ :	0.2	0.3	0.12	0.1	0.2	0.08

If $A=\{x_i/x_i$ is a prime number $\}$, $B=\left\{x_i/x_i<4\right\}$ are two events, then $P(A\cup B)=$

• A. 0.31
• B. 0.62
• C. 0.82
• D. 0.41

Answer 1

Answer: (C)

The given probability distribution for random variable $x$

$X=X_i$	1	2	3	4	5	6
$P\left(X=X_i\right)$	0.2	0.3	0.12	0.1	0.2	0.8

and two events $A=\{x_i\mid x_i$ is a prime number $\}$
$=\{2,3,5\}$
and $B=\left\{x_i\mid x_i<4\right\}=\{1,2,3\}$
So, $P(A\cup B)=P(X=1)+P(X=2)+P(X=3)+P(X=5)$
$=0.2+0.3+0.12+0.2=0.82$