An insurer has a block of business where the number of claims in a year for a policyholder in the block has the following probability distribution.
Two policyholders from this block are randomly selected and observed for a year. It is found that there are exactly four claims for these two policyholders in the past year. What is the probability that one of the policyholders has exactly three claims?
There are two bowls containing red balls and white balls. Bowl 1 contains 5 red balls and 5 white balls. Five balls are randomly selected from Bowl 1 without replacement. Bowl 2 also contains 5 red balls and 5 white balls. Five balls are randomly selected from Bowl 2 with replacement.
If the total number of red balls drawn from the two bowls is eight, what is the expected number of red balls from Bowl 2?