Interpreting Conditional Probability 3

Question

Of all the yoga students in a particular area, 20% study with Patrick and 80% study with Carl. We also know that 8% of the yoga students study with Patrick and are female, while 66% of the students study with Carl and are female. What is the probability that a randomly selected yoga student is female, given that the person studies yoga with Carl?

A. 

0.35

B. 

0.56

C. 

0.69

D. 

0.83

Answer 1

Assume there are x students in total

Then 0.80 x study with Carl

Of these 0.66x are female

So the probability is 0.66x / 0.80 x = 0.66 / 0.80 because we know the person studies with Carl so we are choosing from a group size 0.80x