Question

The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second. The chances of the events are

Moderate

Solution

Let p₁, p₂ be the chances of happening of the first and second events, respectively. Then according to the given conditions, we have
$p_{1} = {p_{2}}^{2}$
and $\frac{1 - p_{1}}{p_{1}} = {(\frac{1 - p_{2}}{p_{2}})}^{3}$
Hence,
$\frac{1 - p_{2}^{2}}{p_{2}^{2}} = {(\frac{1 - p_{2}}{p_{2}})}^{3} or p_{2} (1 + p_{2}) = {(1 - p_{2})}^{2}$
or $3 p_{2} = 1 or p_{2} = \frac{1}{3} and so p_{1} = \frac{1}{9}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

SCAN ME