Bob and will toss two coins. if both coins come up heads, bob pays will $6. will pays bob $2 otherwise. what is the expected value of this game for bob?

Each coin has a head and a tail, therefore when you toss two coins, you have 4 possible outcomes. You have two heads in only one of these outcomes, while the other three have at least one tail.

The expected value of the game is the price paid/gained times the probability of loss/victory:

E = (1 / 4) · (-6) + (3 / 4) · (2)
   = -3 / 2 + 3 / 2
   = 0

Bob expects to tie with Will.