You are playing a game in which a single die is rolled. If a 2 or a 5 comes up, you win $54, otherwise you lose $3. What is the price that you should pay to play the game that would make the game fair?
a. $15 b. $17 c. $7.50 d. $16
2007-12-09 17:15:00 · 5 answers · asked by Chris 1 in Science & Mathematics ➔ Mathematics
(1/3)54 - (2/3)3 = 18 - 2 = 16
2007-12-09 17:20:09 · answer #1 · answered by Philo 7 · 0⤊ 0⤋
D. $16.
1/3 of the time, you win $54.
2.3 of the time, you lose $3 (in the math, that's -$3)
the expected result of playing the game is:
54(1/3) + (-3)(2/3) = 16.
If you play many many times, you can expect to win $16 on average, so to be fair, you should pay $16 each time to play.
2007-12-10 01:23:59 · answer #2 · answered by ladogman 2 · 0⤊ 0⤋
16
2007-12-10 01:21:44 · answer #3 · answered by KingTo H 2 · 0⤊ 0⤋
Let x be the price you should pay.
To make the game fair, your pay should be equal to your loss.
x + (4/6)(3) = (2/6)54
Solve for x,
x = $16
2007-12-10 01:19:19 · answer #4 · answered by sahsjing 7 · 0⤊ 0⤋
two or five is a 2/6 chance to win $54
4/6 chance to lose $3
therefore if you played 6 games theoretically you should win 108
and lose 12
108-12 = 96
96/6 = 16
you should pay $16 to play to be fair
2007-12-10 01:21:04 · answer #5 · answered by Jay 4 · 0⤊ 0⤋