A bowl contains w white balls and b black balls. One ball is selected at random from the bowl, its color noted, and is returned to the bowl along with n additonal balls of the same color. Another ball is randomly selected (now containing w + b + n balls) and is observed black. Show that the conditional probability is w/w+b+n.
The problem should state:
A bowl contains w white balls and b black balls. One ball is selected at random from the bowl, its color noted, and is returned to the bowl along with n additonal balls of the same color. Another ball is randomly selected (now containing w + b + n balls) and is observed black. Show that the conditional probability that the first ball selected was white is w/w+b+n.