Asked by Anna
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
So the answer has to be 5,50euro
Answers
Answered by
Reiny
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,
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,
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.