Question

For two independent events A and B, if P(A) = 0.5 and P(B) = 0.3 , then the value of $100P(A\cup B)$ = ___

Answer 1

We saw that if A and B are two independent events, then $P(A\cap B)=P\left(A\right).P\left(B\right)$
We want to calculate $P(A\cup B)$.
We can calculate this using the relation $P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
Since we can write $P(A\cap B)=P\left(A\right).P\left(B\right)$, we have all the values we need to calculate $P(A\cup B)$
$P(A\cap B)=P\left(A\right).P\left(B\right)$
$=0.5\times 0.3$
$=0.15$
$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$=0.5+0.3-0.15$
$=0.65$
$\Rightarrow 100P(A\cup B)=65$