Question

One of the two events must occur. If the chance of one is $\frac{2}{3}$ 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

The correct option is D

3 : 2

Let P(B) = x

Then, P(A) = $\frac{2x}{3}$

$P\left(A\right)+P\left(B\right)=x+\frac{2x}{3}=\frac{5x}{3}$

$\Rightarrow \frac{5x}{3}=1$ ($\therefore$ They are exhaustive events)

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

Now, $P\left(A\right)=\frac{2}{5}$ and P(B) $=\frac{3}{5}$

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

$=3:2$