Question

$A$ and $B$ are events with $P\left(A\right)=0.5,P\left(B\right)=0.4$ and $P(A\cap B)=0.3$. Find the probability that
neither $A$ and $B$ occurs.

Answer 1

$P\left(A\right)=0.5P\left(B\right)=0.4P(A\cap B)=0.3$

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

$=0.5=0.4-0.3=0.6$

Neither $A$ nor $B$ occurs

$\therefore P{(A\cap B)}^c=1-P(A\cup B)$

$=1-0.6=0.4$ Ans.