Date: Feb 15, 2013 2:16 PM
Subject: Re: probability question about the dice game
>I've lived in the States. I've lived in the UK. People say
>things like "The odds of winning the lottery are millions to one."
In this context, it means "millions to one _against_".
The "against" can be omitted without loss of clarity since the
context makes it clear that it has to be "against".
But when the probabilities are less clear, the odds should be
taken literally, that is,
odds of a to b means a probability of a/(a+b).
If one says,
"The odds are 2-to-1 that it will rain tomorrow"
that means a 2/3 chance of rain.
On the other hand, if one
"The odds are 2-to-1 against rain tomorrow"
that means a 1/3 chance of rain.