1. The probability that Santa put you on the ?Naughty List? this year is 0.78. If you were naughty, the probability that you will get a lump of coal is 0.9. If you were nice, then the chance he will still give you a lump of coal on accident is 0.15. What is the probability Santa put you on the ?Naughty List? given he gives you a lump of coal?
2. There is a game. You flip a coin. If it is a head, you lose $1, and the game is over. If it is a tail, you flip again. On this second flip, if it is a head, you lose $5, and the game is over. If it is a tail, you flip again. On this third flip, if it is a head, you lose $10, and the game is over. If it is a tail, you flip again. On this fourth flip, if it is a head, you lose $20, and the game is over. If it is a tail, you win. How much do you have to win in order to make it a fair game? (Meaning, in the long run, you don?t expect to make or lose money.)
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