Question

Calculating Probability

1. Without looking up their actual birth dates, calculate the probability that Abraham Lincoln and John F. Kennedy were both born in leap years.
2. Without looking up their actual birth dates, calculate the probability that Abraham Lincoln, John F. Kennedy, Ronald Reagan, and George W. Bush were all born in leap years.

Answer 1

I have no idea when any of them were born, but we may assume that all of Abraham Lincoln,John F. Kennedy,Ronald Reagan and George W. Bush were born between 1800 A.D to 1950 A.D.

Now we are to find the number of leap years in the span of (1950-1800), i.e. 150 years.

This is usually given by =37.

Thus the probability of any one of them to be born in a leap year is = (total number of leap years in the given span of years)/(total span of years) = 37/150

Now we can assume that the events of them getting born are independent of each other.

The probability of Abraham Lincoln and John F. Kennedy were both born in a leap year = P(Abraham Lincoln was born in a leap year)P(John F. Kennedy was born in a leap year) = (37/150)(37/150) = (37/150)² = 1369/22500

The probability that Abraham Lincoln, John F. Kennedy, Ronald Reagan, and George W. Bush were all born in leap years = P(Abraham Lincoln was born in a leap year)P(John F. Kennedy was born in a leap year)P(Ronald Reagan was born in a leap year)P(George W. Bush was born in a leap year) = (37/150)(37/150)(37/150)(37/150)=(37/150)⁴ = 1874161/506250000

The probability of Abraham Lincoln and John F. Kennedy were both born in a leap year = 1369/22500

The probability that Abraham Lincoln, John F. Kennedy, Ronald Reagan, and George W. Bush were all born in leap years = 1874161/506250000