Number of boxes you must buy before you can claim the prize

Number of boxes you must buy before you can claim the prize

Consider the following variation of the coupon collector’s problem. Each box of cereal contains one of 2n different coupons. The coupons are organized into n pairs, so that coupons 1 and 2 are a pair, coupons 3 and 4 are a pair, and so on. Once you obtain a coupon from every pair, you can obtain a prize. Assuming the coupon in each box is chosen independently and uniformly at random from the 2n possibilities, what is the expected number of boxes you must buy before you can claim the prize?


 

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