Question

A. 1/5 B. 1/3 C. 7/15 D. 1/2

Answer 1

$P(B|A)=\dfrac{P(A \cap B)}{P(A)}\\\\ |\Omega|=15\cdot14=210\\ |A|=3\cdot14=42\\ |A \cap B|=3\cdot7=21\\\\ P(A)=\dfrac{42}{210}=\dfrac{7}{35}\\ P(A \cap B)=\dfrac{21}{210}=\dfrac{1}{10}\\\\ P(B|A)=\dfrac{\dfrac{1}{10}}{\dfrac{7}{35}}=\dfrac{1}{10}\cdot\dfrac{35}{7}=\dfrac{1}{2}\Rightarrow \text{D}$