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) .35
B) .56
C) .69
D) .83

Answer 1

The probability of selecting a female is 83%

Explanation:

So the correct option is D) 0.83

Answer 2

`P = \text{study with Patrick}`

`C = \text{study with Carl}`

`F = \text{female}`


`\mathbb P(F\mid C)=(\mathbb P(F\cap C))/(\mathbb P(C))=(0.66)/(0.80)=0.825\approx0.83`