Terrible conditional probability problems

[kenny1999]

Homework Statement

This is a problem I found on web but with no solutions.


n Exercise 11 from "Problems on Minterm Analysis," we have the following data: A survey of a represenative group of students yields the following information:
52 percent are male
85 percent live on campus
78 percent are male or are active in intramural sports (or both)
30 percent live on campus but are not active in sports
32 percent are male, live on campus, and are active in sports
8 percent are male and live off campus
17 percent are male students inactive in sports

Let A = male, B = on campus, C = active in sports.

(a) A student is selected at random. He is male and lives on campus. What is the (conditional) probability that he is active in sports?
(b) A student selected is active in sports. What is the(conditional) probability that she is a female who lives on campus?

Homework Equations

The Attempt at a Solution

I have tried. but don't know correct or not.
For (a) I think we are trying to find


P(C | A&B) = P( C & (A&B) ) / P(A&B)

but then I don't know how to find P(A&B). I don't know if A and B are mutually exlusive.

 

[tiny-tim]

hi kenny1999!

two useful tips:

i] use easy-to-recognise letters …

in this case, M for male, C for campus, and S for sport …

that makes it far less likely that you'll make a mistake! ​

ii] before you do anything else, rewrite all the data in terms of M C and S …

what do you get? ​