Problem Contest - Problem of the Week – October 26, 2004
A Two-Stage Game of Chance. A game is played in two stages. First, an ordinary six-sided die is rolled 100 times, and the number of times, N, that a 6 is rolled is observed and recorded: N = n. Next, a fair coin is tossed n times and the random number of tails obtained, M, is observed and recorded: M=m.
- For the entire game, what is the probability that M=m? Hint: The values of m can range from 0 to 100.
- Bonus Question: If the player wins a payout of $m, how much should each player be charged if the charity that runs this game wants to make an average of $1 each time a contestant plays the game?
Submit written solution with justification to John Emerson, Warner 312, before 3:00 on Tuesday, November 2. Or leave them in the Warner mailroom.
Note: Join us at the weekly seminars, usually on Tuesday at 3:00 for refreshments.