another mathematical expectation ?
Bobby and Billy were in the restroom pitching pennies against the bathroom wall again. They put up $4 apiece this time, and if 3H occur first, Bobby gets the $8; if 3T occur first, Billy gets the $8. The game started and the first three tosses were HHT. Just then the principal walked in and ordered the game stopped immediately and that the money be split between Bobby and Billy according to their mathematical expectations from that point in the game. How much money does bobby receive and how much money does Billy receive?
I know that the probability of Bobby winning is 3/4. The question is phrased in a way that is confusing me.
is this just as simple as bobby gets (8)(3/4) and billy gets (8)(1/4)???