Multiple choice

If a leap year is selected at random, what is the chance it will contain 53 Sunday?

  1. probability is $\cfrac{4}{7}$
  2. probability is $\cfrac{3}{7}$
  3. probability is $\cfrac{2}{7}$

  4. none of these
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C Correct answer
Explanation

A leap year has 366 days, which is 52 weeks and 2 days. The extra 2 days can be (Sun, Mon), (Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri), (Fri, Sat), or (Sat, Sun). Out of these 7 possibilities, 2 contain a Sunday.

AI explanation

A leap year has 366 days, which equals 52 weeks and 2 extra days. For the year to have 53 Sundays, one of these two extra days must be a Sunday. The two extra days can be any of 7 combinations: (Sun, Mon), (Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri), (Fri, Sat), or (Sat, Sun). Since 2 out of the 7 possible pairs include a Sunday, the required probability is 2/7.

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