Q.
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 $A=\left\{x_{i} / x_{i}\right.$ is a prime number $\}$, $B=\left\{x_{i} / x_{i}<4\right\}$ are two events, then $P(A \cup B)=$
| $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 |
AP EAMCETAP EAMCET 2019
Solution:
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 $A=\left\{x_{i} \mid x_{i}\right.$ is a prime number $\}$
$=\{2,3,5\}$
and $B=\left\{x_{i} \mid x_{i}<4\right\}=\{1,2,3\}$
So, $P(A \cup B)=P(X=1)+P(X=2)+P(X=3)+P(X=5)$
$=0.2+0.3+0.12+0.2=0.82$
| $X=X_{i}$ | 1 | 2 | 3 | 4 | 5 | 6 |
| $P\left(X=X_{i}\right)$ | 0.2 | 0.3 | 0.12 | 0.1 | 0.2 | 0.8 |