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Question

Find the probability that a leap year selected at random, will contain 53 Sundays?

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Solution

There are 366 days in a leap year that contain 52 weeks and 2 more days. So, 52 Sundays and 2 days.

These 2 days can be:
(Mon, Tue}, {Tue, Wed}, {Wed, Thu}, {Thu, Fri}, {Fri, Sat}, {Sat, Sun} and {Sun, Mon} (7 cases).
In order to have 53 Sundays we should have either {Sat, Sun} or {Sun, Mon} case.
No. of sample spaces = 7.
No. of event that gives 53rd Sunday in Leap Year = 2.

Required Probability = 2⁄7.

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