Help With Conditional Probability Question

I'm trying to find out the probability of A given B. I understand the equation to be: P(A/B) = P(A and B)/P(B)
Assuming that's true, I don't know what I'm supposed to do with the given numbers in the attached picture. Add them? I added them all up and the divided them by what I got for P(B) and I just know it's not right. Help? Thank you.

Idonotknowmath said:

I'm trying to find out the probability of A given B. I understand the equation to be: P(A/B) = P(A and B)/P(B)
Assuming that's true, I don't know what I'm supposed to do with the given numbers in the attached picture. Add them? I added them all up and the divided them by what I got for P(B) and I just know it's not right. Help? Thank you.

Click to expand...

\(\displaystyle \mathcal{P}(A\cap B)=.16\)

Hi, ty, but I'm not looking for the answer here, I'm looking for how you got it so I can actually learn it. Nor is that the correct answer, just so you know? Thank you.

Idonotknowmath said:

I'm trying to find out the probability of A given B. I understand the equation to be: P(A/B) = P(A and B)/P(B)
Assuming that's true, I don't know what I'm supposed to do with the given numbers in the attached picture. Add them? I added them all up and the divided them by what I got for P(B) and I just know it's not right. Help? Thank you.

Click to expand...

Sometimes the easiest way to understand these kinds of questions is to take, say 100 samples [enough to make the given probabilities integers]. Now since we are given B we have 16 in both A and B and 22 in only B for a total of 38 in B. So, given B, are sample is narrowed to 38. The number in both A and B is 16. So, the probability of being in A given that we are in B is 16/38. Now we see where the formula comes from.
P(A given B) = 16/38 = .16/.38 = P(A and B) / P(B)

Idonotknowmath said:

Hi, ty, but I'm not looking for the answer here, I'm looking for how you got it so I can actually learn it. Nor is that the correct answer, just so you know? Thank you.

Click to expand...

pka did not give you the answer - look at it carefully.

He showed you the first step towards the answer. We were hoping you would know enough to get to the next step.

Yes, I can kind of see that now. Sorry for jumping the gun. Can you explain then why it's .16/.38 and why .39 (the sum of A) doesn't factor in here at all? This is alright for finding out THIS question … but I don't think I'll be able to remember it when they give me a whole new question and it's the same concept but it looks totally different.