Solve Probability Problem: Find P(B) & P(A/B)

[chwala]

Homework Statement

$The question is as follows given$P(A/B)=0.8, P(B/A")=0.6$and P(A)=0.75 then find P(B) and$ P(A/B)##[/B]

Homework Equations

The Attempt at a Solution

$P(A/B)= P(AnB)/P(B)$ where$P(AnB)= P(B/A).P(A)= 0.8*0.75=0.6$
$P(A/B)= 0.6/P(B)$ am now stuck here how do i move from here?

 

[Joffan]

Homework Statement

[/B]
Given $P(A/B)=0.8, P(B/A')=0.6$ and $P(A)=0.75$ then find $P(B)$ and $P(A/B)$

Homework Equations

The Attempt at a Solution

$P(A/B)= P(A\land B)/P(B)$ where $P(A\land B)= P(B/A)P(A)= 0.8*0.75=0.6$
$P(A/B)= 0.6/P(B)$ am now stuck here how do i move from here?

looks like you're nearly there... calculate $p(A')$, then can you find $p(A' \land B)$ ?

 

[statdad]

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?
$$\begin{align*} P(A \mid B) & = 0.8 \\ P(B \mid A') & = 0.6 \\ P(A) & = 0.75 \\ \text{Need} & \\ P(B) & \\ P(A \cap B) \text{ (instead of } & P(A \mid B) \text{?)} \end{align*}$$

 

[chwala]

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?
$$\begin{align*} P(A \mid B) & = 0.8 \\ P(B \mid A') & = 0.6 \\ P(A) & = 0.75 \\ \text{Need} & \\ P(B) & \\ P(A \cap B) \text{ (instead of } & P(A \mid B) \text{?)} \end{align*}$$

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)

 

[statdad]

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.