Suppose it costs $35 to roll a pair of dice. You get paid 5 dollars times...

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Question

Suppose it costs $35 to roll a pair of dice. You get paid 5 dollars times...

Suppose it costs $35

to roll a pair of dice. You get paid 5 dollars times the sum of the numbers that appear on the dice. What is the expected payoff of the game? Is it a fair game?

Please show work so I can learn :) Thanks

math Statistics-And-Probability

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Answer 1

Answer #1

here let X is sum of the number on 2 dice:

P(X=2)=P(both dice show 1) =1/36

P(X=3)=2/36

P(X=4)=3/36

P(x=5)=4/36

P(X=6)=5/36

P(X=7)=6/36

P(X=8)=5/36

P(X=9)=4/36

P(X=10)=3/36

P(X=11)=2/36

P(X=12)=1/36

hence expected value on the pair of dice =E(X)=xP(x)

=(2*1/36+3*2/36+4*3/36+5*4/36+6*5/36+7*6/36+8*5/36+9*4/36+10*3/36+11*2/36+12*1/36) =7

as payoff of the game =5X

therefore expected payoff of the game =5*E(X)=5*7 =35

as expected payoff is equal to cost of the game , therefore it is a fair game

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Answer 2

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