Solution
Coupon Collector
Show the problem again
There are 6 distinct coupons, and each cereal box contains one coupon chosen uniformly at random. What is the expected number of boxes you need to purchase to collect all 6 coupons? Give the exact value.
Worked solution
The answer is 14.7. The expected number of boxes to get the kth new coupon, given k−1 already collected, is 6/(6−k+1). Summing over k=1 to 6: 6(1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6) = 6 × 49/20 = 14.7.
Source: The coupon collector's problem, classic in probability since de Moivre and Laplace. Statement written for AxiomIQ.