Answer to Question #135345 in Statistics and Probability for Muhammad Moin

Question

Let A denote the event 'student is female' and let B denote the event 'student is
French'. In a class of 100 students suppose 60 are French, and suppose
that 10 of the French students are females. Find the probability that if I pick a
French student, it will be a girl that is, find P (A|B).

Answer 1

Class has 100 students.

Probability to pick up French is $\displaystyle P(B) =\frac{60}{100}= 0.6$ .

Probability to pick up female French is $\displaystyle P(A\cap B) = \frac{10}{100} = 0.1$.

$\displaystyle P(A|B) = \frac{P(A\cap B)}{P(B)} = \frac{0.1}{0.6}= \frac{1}{6}$

Answer: 1/6.