Question

One of the two events must occur. If the chance of one is 2/3 of the other, then odds in favour of the other are
(a) 1 : 3
(b) 3 : 1
(c) 2 : 3
(d) 3 : 2

Answer 1

(d) 3 : 2

Let P(B) = x
Then, P(A) = $\frac{2x}{3}$
P(A) + P(B) = $x+\frac{2x}{3}=\frac{5x}{3}$
$\Rightarrow \frac{5x}{3}=1$ (∵ They are exhaustive events)
$\Rightarrow x=\frac{3}{5}$
Now, $P\left(A\right)=\frac{2}{5}\mathrm{and}P\left(B\right)=\frac{3}{5}$

∴ Odd in favour of B = $\frac{3/5}{1-3/5}=\frac{3}{2}=3:2$