Question

Probability that a leap year has 53 Sundays is

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

Hint:

Leap Year Sundays. Leap Year = 366 days = 52 weeks + 2 days. The probability of 53 Sundays depends on these 2 extra days. The pairs containing a Sunday are (Sat, Sun) and (Sun, Mon). Probability = 2/7. (For a non-leap year, 365 days = 52 weeks + 1 day, probability = 1/7).

Answer 1

The Correct Option is B

A leap year has 366 days.
Number of weeks in a leap year = \( 366 / 7 \).
$$ 366 \div 7 = 52 \text{ remainder } 2 $$ So, a leap year has 52 complete weeks and 2 extra days.
The 52 complete weeks guarantee 52 Sundays.
The occurrence of the 53rd Sunday depends on the combination of the 2 extra days.
These two extra days can be the following pairs: (Sunday, Monday) (Monday, Tuesday) (Tuesday, Wednesday) (Wednesday, Thursday) (Thursday, Friday) (Friday, Saturday) (Saturday, Sunday) There are 7 possible combinations for these two consecutive days, each equally likely.
The combinations that include a Sunday are (Sunday, Monday) and (Saturday, Sunday).
There are 2 favorable outcomes out of 7 possible outcomes.
Therefore, the probability of a leap year having 53 Sundays is 2/7.