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Suppose it costs $36 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?

Respuesta :

Answer:

-1.833, not a fair game

Step-by-step explanation:

Given that it costs $36 to roll a pair of dice. You get paid 5 dollars times the sum of the numbers that appear on the dice

We have sample space for sum of numbers of dice as

sum       2      3      4      5       6         7      8      9       10      11     12

Prob  1/36  2/36   3/36  4/36 5/36   6/36  5/36  4/36  3/36  2/36  1/36

X gain  10     15     20    25    30       35     40     45      50      55    60

Prob  1/36  2/36   3/36  4/36 5/36   6/36  5/36  4/36  3/36  2/36  1/36

Expected payoff =[tex]\frac{10+30+60+100+150+180+200+180+150+110+60}{36} \\=34.167[/tex]

Cost of playing the game = 36

Net pay off by playing (expected) = [tex]34.167-36\\=-1.833[/tex]

Since expected pay off is negative it is not a fair game.