P(A) = 0.56
P(B|A) = 0.85
P(¬B|¬A) = 0.32
What is P(B)?
Please answer using at least two decimal places.
The correct answer is supposed to be 0.78 but I am completely stumped on finding this. Would really appreciate a breakdown of the process. Please help, thank you in advance.
You're given numbers that relate to $B$, so starting with those and see what falls out might be a good idea. We insert into the respective formulas to get: $$ 0.85 = P(B\mid A) = \frac{P(B\cap A)}{P(A)}\\ 0.32 = P(\lnot B\mid \lnot A) = \frac{P(\lnot B \cap \lnot A)}{P(\lnot A)} $$ This lets you find the probabilities $$P(B\cap A)\\P(\lnot B \cap \lnot A) = 1-P(B\cup A)$$ You should now have a formula which lets you combine these two along with $P(A)$ to find $P(B)$. And if not, then drawing a Venn diagram and marking the regions you now know the probability for should make it evident which ones need to be added / subtracted to give you $P(B)$.