A Coast Guard dispatcher receives an SOS from a ship that has run aground off the shore of a small island. Before the captain can relay her exact position, though, her radio goes dead. The dispatcher has n helicopter crews he can send out to conduct a search. He suspects the ship is somewhere either south in area I (with probability p) or north in area II (with probability 1 − p). Each of the n rescue parties is equally competent and has probability r of locating the ship given it has run aground in the sector being searched. How should the dispatcher deploy the helicopter crews to maximize the probability that one of them will find the missing ship? (Hint: Assume that m search crews are sent to area I and n −m are sent to area II. Let B denote the event that the ship is found, let A1 be the event that the ship is in area I, and let A2 be the event that the ship is in area II. Use Theorem 2.4.1 to get an expression for P(B); then differentiate with respect to m.)