I have been trying to answer this problem but it appears I have the incorrect approach.
Given events $A,B$ with $P(A)=0.5$, $P(B)=0.7$, and $P(A\cap B)=0.3$, find: $P(A'|B')$
I know $P((A\cup B)') = 1 - P(A\cup B)$ I also know that $P(A\cup B) = P(A) + P(B) - P(A\cap B) = 0.5 + 0.7 - 0.3 = 0.9$ Hence $P((A\cup B)') = 1 - P(A\cup B) = 1 - 0.9 = 0.1$
$P(A'|B') = 0.1 / (1-0.7) = 0.3$ but that appears to be the wrong answer. Where am I going wrong?
Thank you in advance!
The only mistake I can find is that $\frac{0.1}{1-0.7}$ is $\frac{1}{3}$ which is $0.333...$ According to me the answer is $\frac{1}{3}$