1) An urn contains n white and m black balls. The balls are withdrawn one at a time until only those of the same color are left. Show that with probability n/(n+m) they are all white.
2) An urn contains 5 white and 10 black balls. A fair die is rolled and that number of balls is randomly chose from the urn. What is the probability that all of the balls selected are white? What is the conditional probability that the die landed on 3 if all the balls selected are white?
1) Total number of balls = n+m
Number of white balls = n
Probability that all n white balls are left back in the urn = n/(n+m)
The solution determines the probability of how many balls are white in the urn.