Question

Find the probability that a leap year selected at random will contain 53 Sundays and 53 Mondays.

Answer 1

Given: A leap year has 366 days = 52 weeks + 2 days, so exactly two weekdays occur 53 times.

Step-wise calculation:

1. The two extra days are a consecutive pair of weekdays determined by Jan 1; there are 7 equally likely pairs: (Sun, Mon), (Mon, Tue), ..., (Sat, Sun).

2. For both Sunday and Monday to occur 53 times the extra pair must be (Sunday, Monday). Only 1 of the 7 possible pairs satisfies this.

Required probability = `1/7`.