How often will at least one hipster pick his own phone ?

1. Four hipsters bump into each other in a crowded elevator and drop their identical cell phones as the elevator doors are closing. In the scramble to retrieve their phones, each hipster picks up a phone at random. How often will at least one hipster pick his own phone? How often will every hipster pick his own phone? What is the most likely number of correct matches of phone to owner? On average, howmany hipsters will pick their own phone?

2. The probability of a random event occurring is defined as the long-run proportion (or relative frequency) of times the event would occur if the random process that generates the event wererepeated a large number of times under essentially identical conditions. A probability can be approximated by simulating the random generating process many times. Simulation leads to an empirical estimate of the probability, which is the proportion of times that the event occurs in the simulated repetitions of the random process