Question

A player rolls two fair dice. He wins $1 if the product is odd and loses...

A player rolls two fair dice. He wins $1 if the product is odd and loses $1 if the product is even. What is the expected value of this game? Is this a fair game?

Math   Statistics-And-Probability   
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Answer #1
Die1 Die2 product
1 1 odd
1 2 even
1 3 odd
1 4 even
1 5 odd
1 6 even
2 1 even
2 2 even
2 3 even
2 4 even
2 5 even
2 6 even
3 1 odd
3 2 even
3 3 odd
3 4 even
3 5 odd
3 6 even
4 1 even
4 2 even
4 3 even
4 4 even
4 5 even
4 6 even
5 1 odd
5 2 even
5 3 odd
5 4 even
5 5 odd
5 6 even
6 1 even
6 2 even
6 3 even
6 4 even
6 5 even
6 6 even
x even(-1) odd(+1)
p(x) 25/36 9/36

=

=(-25+9)/36=-0.444

expected value is -0.4444

this is not fair, expected value is negative

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