Question

A game is played using one die. if the die is rolled and shows 6, the player wins $20. if the die shows any number other than 6, the player wins nothing.
a. if there is a charge of $4 to play the game, what is the game's expected value?
$______(round to the nearest cent)
b. choose the statment below that best describes what this value means.
Choose one!
a. over the long run, the player can expect to lose about this amount for each game played
b. over the long run, the player can expect to win about this amount for each game playedc. over the long run, the player can expect to break even.

Answer 1

A game is played using one die. If the die is rolled and shows 1, the player wins $5. If the die shows any number other than 1, the player wins nothing. If there is a charge of $1 to play the game, what is the game's expected value?

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Let random variable "x" be a count of player gain.

X-values are: 4, -1

P(x=4) = 1/6; P(x= -1) = 5/6

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E(x) = (1/6)(4) + (5/6)(-1)

E(x) = [4-5]/6

E(x) = -1/6 = -17 cents

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Cheers,