Solution: 2015 Winter Final - 12

Author: Michiel Smid

Question

Consider two events $A$ and $B$ in a sample space $S$. You are given that $\Pr(B) = 2/3$ and $\Pr(A|B) = 4/5$. What is $\Pr(A \cap B)$?

(a)

7/15

(b)

6/15

(c)

8/15

(d)

5/15

$ Pr(A|B) = \frac{Pr(A \cap B)}{Pr(B)} $

$ \frac{4}{5} = \frac{Pr(A \cap B)}{ \frac{2}{3}} $

$ Pr(A \cap B) = \frac{4}{5} \cdot \frac{2}{3} $

$ Pr(A \cap B) = \frac{8}{15} $