Question

There are 20 tiles in a bag. Of these, 9 are purple, 5 are black and the rest are white.

Answer 1

$P(B|A)=\dfrac{P(A\cap B)}{P(A)}\\\\ |\Omega|=20\cdot19=380\\ |A|=6\cdot19=114\\ |A\cap B|=6\cdot5=30\\\\ P(A)=\dfrac{114}{380}=\dfrac{3}{10}\\ P(A \cap B)=\dfrac{30}{380}=\dfrac{3}{38}\\\\ P(B|A)=\dfrac{\dfrac{3}{38}}{\dfrac{3}{10}}\\\\ P(B|A)=\dfrac{3}{38}\cdot\dfrac{10}{3}=\dfrac{5}{19}\Rightarrow \text{B}$