Probability of an event in terms of odds for or against the event

Given a probability P(E),

Odds "FOR",

E = P(E)/[1 – P(E)]

e.g. A probability of 20% would be "1 to 4".


Odds "AGAINST",

E = [1 – P(E)]/P(E)

e.g.A probability of 20% would be "4 to 1".