In a game, four coins are rolled. The stake is 2 euros. If 'tail' appears four times, you win 10 euros. If 'tail appears three times, you win x euros. In all other cases you do not win anything and you lose your bet. Determine the value of x so that it would be a fair game.
So the answer has to be 5,50euro
prob(4 tails out of 4) = (1/2)^4
expected value in that case = (1/16)($10) = $.625
prob(3 tails out of 4) = C(4,3)(1/2)^3 (1/2) = 1/4
expected value in that case = (1/4)($x) = x/4
x/4 + .625 = 2
times 4
x + 2.5 = 8
x = 8-2.5 = $5.50
Replace $ with Euros,