Question

If odds against an event be 7 : 9, find the probability of non-occurrence of this event.

 

Answer 1

If the odds against the happening of an event A are a : b, then the probability of not happening of event A = \[P\left( \bar{A} \right) = \frac{a}{a + b}\] It is given that odds against an event are 7 : 9.
Thus, n(S) = 7k + 9k = 16k
and n(E) = 7k
Hence, probability of non-occurrence of this event = \[\frac{n\left( E \right)}{n\left( S \right)} = \frac{7k}{16k} = \frac{7}{16}\]