Question

Given find $P\left(A\right)=\frac{3}{5}andP\left(B\right)=\frac{1}{5}$, find $P\left(A\text{or}B\right)$, if $A$ and $B$ are mutually exclusive events.

Answer 1

Given find $P\left(A\right)=\frac{3}{5}$ and $P\left(B\right)=\frac{1}{5}$,find $P\left(AorB\right)$, if A And B are mutually exclusive events.

solution:

Given $P\left(A\right)=\frac{3}{5}$

$P\left(B\right)=\frac{1}{5}$

since A and B are mutually exclusive,

so,P(A$\cap$ B) = 0

Now,

$P\left(AorB\right)=P(A\cup B)$

we know that

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

putting values

$P(A\cup B)=\frac{3}{5}+\frac{1}{5}-0$

$\Rightarrow P(A\cup B)=\frac{4}{5}$

Hence $P\left(AorB\right)=\frac{4}{5}$.