Conditional Probability

Question

(a)    P(E^C | F)

 

(b)    P(F^C | E)

Any help is appreciated thanks. 

Answer 1

(a) This is the probability that E didn't happen, given that F happened

I assume the Venn diagram shows relative frequency so let's multiply all the numbers by 100 to get the actual frequencies

Then F happened for 15 + 15 = 30 people

Of these people , E didn't happen for 15

So the probability = 15 / 30 = 1/2

(b) This is the probability that F didn't happen, given that E happened

E happened for 20 + 15 = 35 people

Of these F didn't happen for 20

So probability = 20 / 35 = 4/7