Question

SEETA AND GEETA ARE TWO SISTERS WITH AN AGE DIFFERENCE OF 3 YEARS . FIND THE PROBABILITY THAT ;
1.THEY BOTH ARE BORN IN A LEAP YEAR
2. AT LEAST ONE OF THEM IS BORN IN A LEAP YEAR

Answer 1

$$\begin{gathered} \mathrm{Dear}\mathrm{Student}, \\ \mathrm{a}) \\ \mathrm{It}\mathrm{is}\mathrm{known}\mathrm{that},\mathrm{leap}\mathrm{years}\mathrm{comes}\mathrm{after}\mathrm{every}\mathrm{three}\mathrm{years},\mathrm{i}.\mathrm{e}\mathrm{every}4\mathrm{th}\mathrm{year}\mathrm{is}\mathrm{a}\mathrm{leap}\mathrm{year}. \\ \mathrm{Age}\mathrm{Difference}\mathrm{between}\mathrm{Seeta}\mathrm{and}\mathrm{Geeta}\mathrm{is}3\mathrm{years}. \\ \mathrm{Therefore},\mathrm{both}\mathrm{cannot}\mathrm{be}\mathrm{born}\mathrm{in}\mathrm{leap}\mathrm{year}. \\ \mathrm{Probability}(\mathrm{both}\mathrm{are}\mathrm{born}\mathrm{in}\mathrm{leap}\mathrm{year})=0 \\ \mathrm{b}) \\ \mathrm{Further},\mathrm{the}\mathrm{age}\mathrm{difference}\mathrm{is}3,\mathrm{therefore}\mathrm{it}\mathrm{can}\mathrm{be}\mathrm{said}\mathrm{that}\mathrm{if}\mathrm{one}\mathrm{is}\mathrm{bornm}\mathrm{in}\mathrm{leap}\mathrm{year}, \\ \mathrm{the}\mathrm{other}\mathrm{will}\mathrm{be}\mathrm{born}\mathrm{in}\mathrm{non}\mathrm{leap}\mathrm{year}. \\ \mathrm{Probability}(\mathrm{atleast}\mathrm{one}\mathrm{is}\mathrm{born}\mathrm{in}\mathrm{leap}\mathrm{year})=\frac{1}{2} \end{gathered}$$