Originally Posted by Richard Davis
If we have a raffle involving 10 tickets, and we sell all 10 tickets, and choose out of the barrel 1 ticket to take the prize, then there are 9 people who will NOT win the prize and 1 person who WILL win the prize. That translates to 1 in 10 odds, not 1 in 9. That's because 10 tickets were sold, not 9.
Well then, if I say 9/10 people will not win a raffle of 10 tickets, and 1 person will, that translates to odds of 1/10 winning. Do you agree?
It isn't 1 in 9 will win. 1/10 will win.
I am curious Rich, if you are able to acknowledge that
as a matter of mathematics, the odds in your example above are in fact 1 to 9 odds.
By definition: odds = the ratio of the probability of something happening to the probability of that something not happening. (citation in earlier post).
* probability of picking winning ticket, one try, your example = 1/10 = 0.1
* probability of not picking winning ticket = 9/10 = 0.9 (expanded form is : ((1 - 0.1) = 0.9)
* odds by definition = 0.1/0.9 (citation in earlier post)
* expanded form, as James pointed out, odds = 0.1/(1-0.1) = 0.1/0.9
* odds therefore are by mathematical definition 1/9, most correctly pronounced as "odds of 1 to 9"
Go ahead and literally make my day. Acknowledge that as a matter of mathematics, the odds in your example above are in fact 1 to 9 odds.