SOLUTION: Consider a game where 2 coins are tossed. $2 is bet on every 2 tosses and we win $4 in both coins land on heads.
(a) What are the expected winnings?
(b) Is this a f
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Question 710366: Consider a game where 2 coins are tossed. $2 is bet on every 2 tosses and we win $4 in both coins land on heads.
(a) What are the expected winnings?
(b) Is this a fair game? If not, what amount should we bet to make it fair?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Consider a game where 2 coins are tossed. $2 is bet on every 2 tosses and we win $4 in both coins land on heads.
P(2 heads) = (1/2)^2 = 1/4
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(a) What are the expected winnings?
Random number vales::: -2......+2
Probabilities:::::::: (3/4)....(1/4)
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E(x) = -2(3/4) + 2(1/4 = [-6+2]/4 = -$1.00
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(b) Is this a fair game?
It is not a fair game because you can expect to lose $1.00 each time you play.
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If not, what amount should we bet to make it fair?
Let the cost to play be "x" and you win $4.00 for 2 heads:
Random value:::: -x......4-x
Probabilities::::(3/4)...(1/4)
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Let E(x) = 0 to make the game fair.
E(x) = (-3/4)x + (1/4)(4-x) = 0
[-3x + 4-x]/4 = 0
-3x+4-x] = 0
x = 1 (You should pay $1 to play the game)
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Cheers,
Stan H.
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