Here are the answers to some of the questions

- 14.7. The first time you roll the dice, you will always get one of the six numbers you're looking for, so the average number of times that you will have to roll the die before one number comes up is 1. The probability of getting a different number the next time you roll the die is 5⁄6, so the number of times you will have to wait for the next number is 6⁄5. Similarly, for the third number you'll have to wait 6⁄4 rolls, and so on. So, the total is
6⁄6 + 6⁄5 + 6⁄4 + 6⁄3 + 6⁄2 + 6⁄1 = 14.7
- This problem can be tackled in the same manner as the above problem. To get the answer, you would sum 18⁄18 + 18⁄17 + 18⁄16 + ... + 18⁄2 + 18⁄1. You will have to open approximately 62.9 packs.
- Approximately 35.9 packs.
- If you assume that each pack can contain duplicates, you can treat each card in each pack as an independent random event and we can proceed in the same manner as the first 3 problems. The end result is approximately 382.9 packs.