Question

What is the probability that a leap year when selected at random, contains 53 Sundays?

• A. 2/7
• B. 1/7
• C. 4/7
• D. 3/7

Answer 1

The correct option is A 2/7

A leap year contains 366 days.

If the first day of the leap year is a Monday, then Monday and Tuesday will occur 53 times and Wednesday, Thursday, Friday, Saturday, and Sunday will each occur 52 times.

So there are 7 possible cases:

1. Leap year starts on a Monday, result: 53 Mondays and 53 Tuesdays.
2. Leap year starts on Tuesday: 53 Tuesdays and 53 Wednesdays.
3. Leap yr. begins Wednesday: 53 Wednesdays and 53 Thursdays.
4. Leap yr. begins Thurs.: 53 Thursdays and 53 Fridays
5. Leap year begins Fri.: 53 Fridays and 53 Saturdays
6. Leap year begins Sat.: 53 Saturdays and 53 Sundays
7. Leap year begins Sun.: 53 Sundays and 53 Mondays.

So, 2 possibilities of having 53 Sundays
p( 53 Sundays in leap year) = $\frac{2}{7}$