Dice Roll Probabilities

Homework Question:
I am not sure if I did it right. If its wrong can you tell me which direction I should be going to?

q7.PNG
a) p=310/1000 =0.31
odds for 31/100
b) p=600/1000 =0.6
odds for 3/5
Tommy AndersonAsked:
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KimputerConnect With a Mentor Commented:
You're good to go, nothing extra needed to explain. I.E. good job.
Though, the more official notation for odds are like this:
3:5 (Three in Five chance, or three to five odds)
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ShannonEECommented:
Hi there Tommy,

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
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KimputerCommented:
@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.
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