How do you calculate your odds of winning at lotto if you spend 1 dollar on an entry?

Answer 1

Odds are expressed as a ratio of probability of winning versus probability of not winning. Consider a simple example of tossing a fair dice where you "win" if it lands on three. P(three):P(not three) = (1/6) : (5/6) = 1:5 . So your odds of winning are 5 to 1 against. Now let's imagine to win lotto you need to guess 6 numbers correctly out of 45 and each guess costs $1. Probability of winning (from 1 guess) = 1/(45 x 44 x 43 x 42 x 41 x 40) = 0.000000000171 Probability of not winning = 1-P(winning) = 0.999999999829 So the odds are 0.000000000171:0.999999999829 = 1:5,864,443,199 or just under 6 billion to 1 against!