MHB Conditional Probability with 3 Events

[Math1015]

I'm currently stuck on a question that involves conditional probability with 3 events. This is a concept that I'm having the most trouble grasping and trying to solve in this subject. I am not sure how to start this problem.

The Question:
Given that P(A n B) = 0.4, P(A n C) = 0.2, P(B|A)=0.6 and P(B)=0.5, find the following.
a) P(A|B)
b) P (B')
c) P(A)
d) P (C|A)
e) the odds in favor of B

If someone could provide an explanation on how to solve this and guide me through it, that would be greatly appreciated! I really want to understand how to do problems like these.

 

[HallsofIvy]

$P(A|B)= \frac{P(A\cap B)}{P(B)}$. You are given that $P(A|B)= 0.6$ and that $P(A\cap B)= 0.4$ so $0.6= \frac{.4}{P(B)}$. $P(B)= \frac{0.4}{0.6}= \frac{2}{3}$. "(e) the odds in favor of B" are "2 out of 5" and "(b) P(B')= 1- 2/3= 1/3".

 

[Math1015]

Thanks for the fast reply! We have an exam on monday and I've been stuck on this all day and understand it better now!