Odds in favor of A = P(A) : P(A') = P(A) / (1 - P(A))

If odds in favor are m:n, then P(A) = $\frac{m}{m+n}$.

Example: Odds of winning are 3:7. Then P(win) = $\frac{3}{3+7}$ = 3/10.

Odds against A = P(A') : P(A) = (1 - P(A)) / P(A)

If odds against are m:n, then P(A) = $\frac{n}{m+n}$.

This conversion appears occasionally in JEE when problems state odds instead of probabilities directly.