Answer to Question #142219 in Statistics and Probability for Seteka

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 a ball now drawn from the second bag is bla

Answer 1

We have two possible cases: a white ball was taken out of the first bag, then the second bag will have 4 white and 2 black balls, or a black ball will have 3 white and 3 black balls in the second bag. Calculate the probability of these events by dividing the number of balls of the desired color by the total number of balls:

$P=\frac{5}{9}*\frac{2}{6}+\frac{4}{9}*\frac{3}{6}=\frac{11}{27}$