# Probability problem

1. Nov 19, 2014

1. The problem statement, all variables and given/known data $The question is as follows given$P(A/B)=0.8, P(B/A")=0.6$and P(A)=0.75 then find P(B) and$ P(A/B)$2. Relevant equations 3. The attempt at a solution$P(A/B)= P(AnB)/P(B) $where$ P(AnB)= P(B/A).P(A)= 0.8*0.75=0.6P(A/B)= 0.6/P(B)$am now stuck here how do i move from here? 2. Nov 19, 2014 ### Joffan looks like you're nearly there... calculate$ p(A') $, then can you find$ p(A' \land B)## ?

3. Nov 19, 2014

If you are given $P(A \mid B)$ why do you need to calculate it?

To be clear: are these the items you are given and the items you are to find?
\begin{align*} P(A \mid B) & = 0.8 \\ P(B \mid A') & = 0.6 \\ P(A) & = 0.75 \\ \text{Need} & \\ P(B) & \\ P(A \cap B) \text{ (instead of } & P(A \mid B) \text{?)} \end{align*}

4. Nov 20, 2014

### chwala

sorry the terms given are P(B/A)= 0.8 , P(B/A")=0.6 and P(A)=0.75 I need to find P(A/B) and P(B)

5. Nov 21, 2014

Well, if you have $P(B \mid A)$ and $P(A)$ you can calculate $P(A \cap B)$ . You can also find $P(A')$ and
then get $P(A' \cap B)$. What will $P(A \cap B)$ and $P(A' \cap B)$ together get you? Once you have that you can finish the questions.