If the odds in favour of an event are 2 1 what is the probability of its happening

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

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 = \[\frac{n\left( E \right)}{n\left( S \right)} = \frac{2k}{5k} = \frac{2}{5}\]

Concept: Event - Occurrence of an Event

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