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.

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

i)    $P$($A$  does not occur) = $P\left(\overline{A}\right)=1-P\left(A\right)=1-\frac{1}{2}=\frac{1}{2}$

ii) $P$( neither $A$ nor $B$occur)  $=P(\overline{A}\cap \overline{B})$

$=P\left(\overline{A\cup B}\right)=1-P(A\cup B)$

$=1-\left[P\right(A)+P(B)-P(A\cap B\left)\right]=1-(0.5+0.4-0.3)$

$=1-0.6=0.4$