Tommy Anderson
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Dice Roll Probabilities
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@ShannonEE is correct for the odds, I glanced over it too quickly. Please post your answer for the odds again to check if you understood it correctly.
Your empirical probabilities are correct, but the odds are not.
odds = prob / (1 - prob)
so that for prob = 1/2, the odds are
(1/2) / (1 - 1/2) = (1/2) / (1/2) = 1: 1
further,
If prob = 0.1 then odds given by
0.1 - (1 - 0.1)
= 0.1 / 0.9
= 1 / 9
= 1 : 9
=======
Another way of thinking about it is
empirical probability = (count of positive outcome) / (total count)
empirical odds = (count of positive outcome) / (count of negative outcome)
or
empirical odds = (count of positive outcome) : (count of negative outcome)
For the odds you cancel out any commen factors -
That is you don't say 6 : 102 but rather 3 : 51 (cancelling out by 2) further reduced to 1 : 17 (cancelling out top and bottom by 3)
You should be able to get the correct answers using the above information.
Ian