Question

The probability that in a year of 22nd century chosen at random, there will be 53 Sunday, is
(a) 3/28
(b) 2/28
(c) 7/28
(d) 5/28

Answer 1

​P(53 Sundays in a leap year) = $\frac{2}{7}$

P(53 Sundays in a non-leap year) = $\frac{1}{7}$

There will be 24 leap years in the 22nd century, i.e. from the year 2201 to 2200, we will have 24 leap years.

∴ P(leap year) = $\frac{24}{100}$

P(non-leap year) = $\frac{76}{100}$

Now,

P(53 Sundays) = P(leap year)$\times$P(53 Sundays in a leap year)
+ P(non-leap year)$\times$P(53 Sundays in a non-leap year)

$$\begin{gathered} =\frac{24}{100}\times \frac{2}{7}+\frac{76}{100}\times \frac{1}{7} \\ =\frac{48}{700}+\frac{76}{700} \\ =\frac{124}{700} \\ =\frac{31}{175} \end{gathered}$$


Disclaimer: None of the given options is correct.