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
i) A does not occur
ii) neither A nor B occurs

Answer 1

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

$1)A$ does not occur $⟹B-A=B-(A\cap B)$

$P(B-A)=P\left(B\right)-P(A\cap B)=0.4-0.3=0.1$

$2\left)P\right($ neither $A$ nor $B)=1-P(A\cup B)=1-P(A)-P(B)+P(A\cap B)=1-0.5-0.4+0.3=0.4$