Question

Find the missing probability. P(A) = 0.4; P(B) = 0.7; P(A or B) ; P(A and B) = 0.3

Answer 1

Given:

$P(A)=0.4, P(B)=0.7, P(A\text{ and }B)=0.3$

To find:

The value of $P(A\text{ or }B)$.

Solution:

We know that,

$P(A\text{ and }B)=P(A\cap B)$

$P(A\text{ or }B)=P(A\cup B)$

It means, we have $P(A)=0.4, P(B)=0.7, P(A\cap B)=0.3$ and we need to find the value of  $P(A\cup B)$.

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

$P(A\cup B)=0.4+0.7-0.3$

$P(A\cup B)=1.1-0.3$

$P(A\cup B)=0.8$

Therefore, the value of $P(A\text{ or }B)$ is 0.8.