A) \[\frac{1}{9},\,\frac{1}{3}\]
B) \[\frac{1}{16},\,\frac{1}{4}\]
C) \[\frac{1}{4},\,\frac{1}{2}\]
D) None of these
Correct Answer: A
Solution :
Let \[{{p}_{1}},\,\,{{p}_{2}}\] be the chances of happenig of the first and second event respectively, then according to the given conditions, we have \[{{p}_{1}}=p_{2}^{2}\] and \[\frac{1-{{p}_{1}}}{{{p}_{1}}}={{\left( \frac{1-{{p}_{2}}}{{{p}_{2}}} \right)}^{3}}\] \[\Rightarrow {{p}_{2}}=\frac{1}{3}\] and so \[{{p}_{1}}=\frac{1}{9}.\]
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