(solution) 1. The probability that Santa put you on the "Naughty List"

(solution) 1. The probability that Santa put you on the "Naughty List"

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.)