Question

The probability of not getting 53 Tuesdays in a leap year is:

• A. \(\frac{2}{7}\)
• B. \(\frac{1}{7}\)
• C. 0
• D. \(\frac{5}{7}\)

Hint:

When calculating probabilities in scenarios involving days of the week or cycles, it's useful to identify the total number of possible outcomes and then determine the favorable outcomes. In this case, the extra days in a leap year determine whether there will be an additional Tuesday. By listing the possible pairs of extra days, you can easily count the favorable cases and compute the probability accordingly.

Answer 1

The Correct Option is D

A leap year has 366 days, equivalent to 52 full weeks and 2 additional days.
These two extra days can be any consecutive pair of days of the week:

• Sunday and Monday
• Monday and Tuesday
• Tuesday and Wednesday
• Wednesday and Thursday
• Thursday and Friday
• Friday and Saturday
• Saturday and Sunday

For a leap year to contain 53 Tuesdays, one of the two extra days must be a Tuesday. The favorable combinations are:

• Monday and Tuesday
• Tuesday and Wednesday

Therefore, the probability of observing 53 Tuesdays in a leap year is calculated as: \(\frac{2}{7}\)
Consequently, the probability of not observing 53 Tuesdays is: \(\frac{5}{7} = 1 - \frac{2}{7}\)
This confirms the probability of not getting 53 Tuesdays in a leap year is: \(\frac{5}{7}\)