Question 1185121

odds for = probability for / probability against.
odds against = probability against / probability for.


example;


if probability of an event is .25, then:


odds for = .25 / .75 = 1/3.
odds against = .75 / .25 = 3/1.


and:


probability of winning is .25 / (.25 + .75) = .25 / 1 = 1/4.
probability of losing is .75 / (.25 + .75) = .75 / 1 = 3/4.



if the probability of an event occurring is .052, then:
the probability of that event not occurring is 1 - .052 = .948.


the odds of that event occurring is .052 / .948.


the odds against that event occurring is .948 / .052.


in whole numbers, these ratios becomes:


odds for = 52 / 948
odds against = 948 / 52


these ratios can be simplified to:


odds for = 13 / 237
odds against = 237 / 13


probability for = 13 / (237 + 13) = 13 / 250 = .052
probability against = 237 / (13 + 237) = 237 / 250 = .948


you take .052 / .948 and multiply both sides by 1000 aqnd you get 52 / 948.
that's where the whole numbers come from.


here's a reference on odds versus probabilities.


<a href = "https://www.thoughtco.com/how-are-odds-related-to-probability-3126553" target = "_blank">https://www.thoughtco.com/how-are-odds-related-to-probability-3126553</a>