Question

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

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

Answer 1

Answer: (D)

$\frac{5}{7}$

Answer 2

In a leap year, there are 366 days. Since 366 days = 52 full weeks + 2 extra days, the extra days can either be Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, or Saturday. Therefore, there are exactly 52 Tuesdays in a leap year, and the extra two days will contribute to the possibility of having an additional Tuesday.

For the probability of not having 53 Tuesdays, the extra two days must not include a Tuesday. The possible pairs of extra days are: Sunday-Monday, Monday-Tuesday, Tuesday-Wednesday, Wednesday-Thursday, Thursday-Friday, Friday-Saturday, Saturday-Sunday. Out of these, only the pair Monday-Tuesday, Tuesday-Wednesday include a Tuesday.

So, the probability of not getting 53 Tuesdays is:

$P(\text{not getting 53 Tuesdays}) = \frac{5}{7}$.

Thus, the correct answer is:

$\frac{5}{7}$.