## Coupon Collecting Problem: Find the Expectation of Boxes to Collect All Toys

## Problem 750

A box of some snacks includes one of five toys. The chances of getting any of the toys are equally likely and independent of the previous results.

**(a)** Suppose that you buy the box until you complete all the five toys. Find the expected number of boxes that you need to buy.

**(b)** Find the variance and the standard deviation of the event in part (a).