Question

If the probability of the occurrence of a certain event E is $\frac{3}{11}$, find

(i) The odds in favour of its occurrence. and

(ii) The odds against its occurrence.

Answer 1

Let there be m outcomes favourable to E and n outcomes unfavourable to E. Then,

$P\left(E\right)=\frac{m}{m+n}\Rightarrow \frac{m}{m+n}=\frac{3}{11}$ $[\because P(E)=\frac{3}{11}\text{given}]$

$\Rightarrow m=3$ and $n=8$

(i) Odds in favour of E $=\frac{m}{n}=\frac{3}{8}$

(ii) Odds against E $=\frac{n}{m}=\frac{8}{3}$