Answer to Question #142177 in Statistics and Probability for Florence Sapezo

Question

One bag contains 5 white balls and 4 black balls and the second bag contains 3 white balls and 2 black balls.one ball is drawn from the first bag and placed unseen in the second bag. What is the probability that the ball now drawn from the second bag is black?

Answer 1

$P(B_2)=P(B_2\cap B_1)$ or$P(B_2\cap W_1)$

$P(B_2\cap B_1)=\frac{3}{6}×\frac{4}{9}=\frac{2}{9}$

$P(B_2\cap W_1)=\frac{2}{6}×\frac{5}{9}=\frac{5}{27}$

$P(B_2)=\frac{2}{9}+\frac{5}{27}=\frac{11}{27}$