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 event are

• A.
• B.
• C.
• D.
  

Answer 1

The correct option is A

Let p₁ and $p_2$ be the chances of happening of the first and second events, respectively, then according to the given conditions, we have
$p_1=P_2^{2}and\frac{1-p_1}{p_1}={\left(\frac{1-p_2}{p_2}\right)}^{3}or\frac{1-p_2^2}{p_2^2}={\left(\frac{1-p_2}{p_2}\right)}^{3}or{p}_2(1+p_2)=(1-p_2{)}^{2}or{p}_2=\frac{1}{3}andso{p}_1=\frac{1}{9}$