## Applied Statistics and Probability for Engineers, 6th Edition

$B'$ and $A'$ are independent events
If $A'$ and $B'$ are independent, then $P(A'\cap B)= P(A')\times P(B)$. LHS= $P(A'\cap B)=P(B)-P(A\cap B)$. $P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}=0.3$ $P(A\cap B)=0.3\times 0.8=0.24$ $P(A'\cap B)=0.8-0.24=0.56$ RHS=$P(A')\times P(B)=(1-0.3)\times 0.8=0.56$