Question

One of the two events must happen. Given that the chance of one is two -third of the other, find the odds in favour of the other.

Answer 1

Let the given events be A and B

Now, P(A) = $\frac{2}{3}P\left(B\right)$

Let P(B) = x

$\therefore P\left(A\right)=\frac{2}{3}x$

The events A and B are exhaustive

$\therefore$ P(A) or P(B) = 1

$\Rightarrow P\left(A\right)+P\left(B\right)=1$

[$\because$ A and B are mutually exclusive]

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

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

$\therefore P\left(B\right)=\frac{3}{5}$

This implies that the odds in favour of B are 3: (5-2) i.e., 3:2