Gaining an intuition for Conditional Probability Questions Building on my same problem in the question I posted here and the following question, I've realized I seem to be unable to tell when the question is asking me to find the $P(A|B)$ or $P(AB)$ for some event $A$ and $B$. The question is "Bev can either take a course in computers or in chemistry. If Bev takes the computer course, then she will receive an A grade with probability 1/2; if she takes the chemistry course then she will receive an A grade with probability 1/3. Bev decides to base her decision on the flip of a fair coin. What is the probability that bev will get an A in Chemistry?"
Its a simple question, but as stated above, I solved for $P\text{(She gets an A|She takes Chemistry)}$ when they actually want $P\text{(She gets an A and She takes Chemistry)}$. I realize this is a fundamental part of probability, but I am struggling to tell the difference and was wondering how to really rectify this issue.
Thanks
 A: I think the best way is to draw the tree diagram of the relevant part. In skeleton form,
P(Took Chem) $(1/2)\rightarrow$ P(Got $A|\text{took chem)} (1/3)\rightarrow$ P(Took Chem$\;\cap$ Got A) = $(1/2)(1/3)$

You could also pay more attention to the wordings.
If ... takes Chem then probability of $A$ 
clearly means $P(A|\text {takes Chem})$
and probability of $A$ in Chem clearly implies the occurrence of both events.
A: I don't know if this answers the question, but I think when working with 'basic' probability questions like this, you need to write out exactly what is being asked of you. The statement is:
"What is the probability that bev will get an A in Chemistry" 
Okay, lets dissect this. There is definitely a $P$ in there, so lets try to put into symbols:
$P$("bev will get an A in chemistry"). 
In this case, we see that there are two sets: Bev gets an A, Bev takes chemistry, and they both have to be true at the same time. There is actually not a single condition in the statement. If is not worded as "What is the probability that if Bev takes chemistry, she gets an A" - you already know this, its in the question! 
You really need to make sure that the statement you are given is reduced to what it actually says.
