Suppose someone gives you 8 to 2 odds that you cannot roll two
even numbers with the roll of two fair dice. This means you
win $8 if you succeed and you lose $2 if you fail. What is
the expected value of this game to you? Should you expect to
win or lose the expected value in the first game? What can
you expect if you play 200 times? Explain.(The table
will be helpful in finding the required probabilities.)
Table of outcomes and sums for the roll of two dice
1
2
3
4
5
6
1
1+1=2
1+2=3
1+3=4
1+4=5
1+5=6
1+6=7
2
2+1=3
2+2=4
2+3=5
2+4=6
2+5=7
2+6=8
3
3+1=4
3+2=5
3+3=6
3+4=7
3+5=8
3+6=9
4
4+1=5
4+2=6
4+3=7
4+4=8
4+5=9
ββ
4+6=10
5
5+1=6
5+2=7
5+3=8
5+4=9
ββ
5+5=10
ββ
5+6=11
6
6+=7
6+2=8
6+3=9
ββ
6+4=10
ββ
6+5=11
ββ
6+6=12
What is the expected value of this game to you?
$__?
Should you expect to win (or lose) an amount equal to the
expected value in the first game?
Yes, you can expect to win (or lose) the expected value in
the first game.
No, the outcome of one game cannot be predicted.
What can you expect if you play 200 times?
$___
Explain this result.
Averaged over 200 games, you should expect to __ $__.