Question

you are given 4 to 1 odds against three heads with three coins , meaning you win $4 if you succeed and you lose $1 if you fail. find expected value of game . what would you expect to win in 1 game or 100 games?

I understand the formula for finding the expected value . what i am having trouble with is putting the information into the equation regarding where it gets

put into the equation

Answer 1

The expected value of a single game is computed here as:

= P(3 heads in 3 tosses)*(Winning Amount) + [ 1 - P(3 heads in 3 tosses)] * (Losing amount )

= 0.53 * 4 + (1 - 0.53)*( - 1)

= 0.5 - 0.875

= -0.375

Therefore -0.375 is the expected amoutn we would win in a single game. That is on an average we would lose $0.375 in a single game.

The expected value for 100 games would be just 100 times the expected value of a single game. Therefore we would be expected to lose $37.5 in 100 games.