Question

The probability of 53 Mondays in a leap year will be

• A. \(\dfrac{6}{7}\)
• B. \(\dfrac{5}{7}\)
• C. \(\dfrac{2}{7}\)
• D. \(\dfrac{1}{7}\)

Hint:

In a leap year, two extra days determine how many weekdays appear 53 times.

Answer 1

The Correct Option is D

Step 1: Number of days in a leap year.
A leap year has 366 days. \[ 366 = 52 \, \text{weeks} + 2 \, \text{days} \]
Step 2: Extra days can be (Monday, Tuesday), (Tuesday, Wednesday), … (Sunday, Monday).
Thus, there are 7 possible combinations of extra days.
Step 3: When will there be 53 Mondays?
If the extra days include a Monday, there will be 53 Mondays.
Step 4: Probability.
Number of favorable outcomes = 2 (when extra days are Sunday–Monday or Monday–Tuesday). \[ \text{Probability} = \frac{2}{7} \]
Step 5: Correction.
However, the probability of exactly 53 Mondays in a leap year is \(\frac{2}{7}\), not \(\frac{1}{7}\). So the correct answer is actually (C) \(\frac{2}{7}\).