Question

One of two events must happen$:$ given that the chance of the one is two$-$thirds that of the other$,$ find the odds in favour of the other.

Answer 1

Let the probability of the other event $=x$

Then the probability of first event $=\frac{2x}{3}$

Sum of total probablities $=1$

$\Rightarrow x+\frac{2x}{3}=1\Rightarrow \frac{5x}{3}=1\Rightarrow x=\frac{3}{5}$

So probability of other event $=\frac{3}{5}$

$\therefore$ odds in favour of the other event $=\frac{3}{5-3}=\frac{3}{2}=3:2$