Question

A mathematics major returns to his apartment one night after heavy drinking and very desperately needs to get inside. Since his vision is blurry, he cannot determine which of the 15 keys that he has will unlock his door. He tries to unlock his door with one key after another, each chosen at random from the bunch at hand. Keys that are found unsuitable are not removed from the bunch and may be chosen and tried again. Suppose that, due to fumbling around, it takes 1.50 minutes to try each key. Find the expected time before the door is unlocked. Round your answer to the nearest tenth.

Answer 1