Question

If odds in favour of an event be 2 : 3, find the probability of occurrence of this event.

Answer 1

If odds in favour of an event A are a : b, then probability of happening of event A = P(A) = $\frac{a}{a+b}$
It is given that the odds in favour of an event are 2 : 3.
Thus, n(S) = 2k + 3k = 5k and n(E) = 2k
Hence, probability of occurrence of this event = $\frac{n\left(E\right)}{n\left(S\right)}=\frac{2k}{5k}=\frac{2}{5}$