Question

From 1900 to 2000 what is the probability that any randomly picked year will have 53 sundays, including both years.

Answer 1

Answer:

The probability is 90 percent.

Answer 2

Every year has 52 weeks and 1 day.

In case of leap year, It will be 52 weeks and 2 days.

We have years from 1900 to 2000,

So total years = 101 including both.

Leap years are 1904, 1908,... 2000. We can observe that there are 25 leap years and 76 normal years.

In a normal year, The probability of 53 sundays is 1/7 ( We have 52 weeks and one day. )

In a leap year, The probability of 53 sundays is 2/7 ( We have 52 weeks and 2 days)

So, If a year is picked at random from 1900 to 2000 both included,

The probability that year does have 53 sundays is

$= \dfrac{ 25\frac{2}{7} + 76 \frac{1}{7} }{101} \\ \\ = \frac{ \frac{50 + 76}{7} }{101} \\ \\ = \frac{126}{707} \\ \\ = \frac{18}{101}$

Therefore, the probability that any randomly picked year from 1900 to 2000 will have 53 sundays, including both years is 18/101.