A storeowner wants to get rid of 25 fireworks from last year in the coming New Year’s season. The manufacturer guarantees that 60% of the fireworks—in this case, 15 units—will ignite after a year. Let us assume that firework functionality is independent and thus follows a hypergeometric distribution. Given this information, let us assume that a customer buys five of the 25 fireworks.

(a) What is the probability that only one firework will ignite?

(b) Assume that the storeowner has 1000 fireworks from the previous year and a customer buys 50 of them. Once again, firework functionality is guaranteed to be 60%. Which distribution would you assume to determine the probability that a certain number of fireworks ignite if you didn’t have a calculator to determine the actual distribution? Explain your answer. You don’t need to perform the calculation here.