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

$P = \text{study with Patrick}$
$C = \text{study with Carl}$
$F = \text{female}$

$\mathbb P(F\mid C)=\dfrac{\mathbb P(F\cap C)}{\mathbb P(C)}=\dfrac{0.66}{0.80}=0.825\approx0.83$