The chance of one event happening is the square of the chance of a second event, but the odds against the first are cube of the odds against the second. The chance of the first event is

Let the two events be E1 andE2 . Let their chances be p and q respectively. Then p=q2 …………….(i)  The chances of not happening of the events are 1−p and 1−q respectively.Odds against the first event = 1−pp Odds against the second event = 1−qq Given 1−pp  =(1−qq)3⇒1−q2q2=(1−q)3q3[from   (i)] ⇒(1−qq2)[(1+q)−(1−q)2q]=0  ∵q≠1  and  q≠0 ∴q(1+q)=1−2q+q2⇒q=13 ∴ from (i) p=q2=19 ∴p(E1)=p=19