[Math Lair] Baseball Cards

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  1. [Baseball card of Cap Anson](Warm-up question) You have a regular six-sided die. What is the average number of times that you will have to roll the die before all six numbers turn up at least once?
  2. There is a set of baseball cards that contains special autographed cards, one per pack. There are 18 autographed cards in total to collect. Assuming the autographed cards are inserted randomly, what is the average number of packs that you will need to buy?
  3. Same as above, only you decide that, after you get 16 different cards, you will trade for the remaining two. How many packages will you need to open, on average?
  4. There is a set of baseball cards that contains 792 cards. There are 15 cards in a pack. On the average, how many packs will you need to open to complete the set? Assume that the contents of each pack are independent of the contents of any other pack. For an easier challenge, assume that a pack can contain more than one of the same card and that the cards in a pack are selected independent of each other (if you want an extra-difficult challenge, try the problem assuming that each pack contains 15 different cards).
[Red Nelson baseball card]

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