Question

The probability that a leap year selected at random will contain either 53 thursdays or 53 fridays is:

• A. 5/7
• B. 4/7
• C. 3/7
• D. 2/7

Answer 1

The correct option is C 3/7

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, 3 possibilities of having 53 thursdays or 53 fridays
p(53 thursdays or 53 fridays in leap year) = $\frac{3}{7}$