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Question

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

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Solution

A leap year has 366 days, therefore 52 weeks i.e. 52 Sunday and 2 days. The remaining 2 days may be any of the following:

Sunday and Monday
Monday and Tuesday
Tuesday and Wednesday
Wednesday and Thursday
Thursday and Friday
Friday and Saturday
Saturday and Sunday

For having 53 Sundays in a year, one of the remaining 2 days must be a Sunday.

Let E be an event of getting 53 Sundays

n(S)=7,n(E)=2

Then, P(E)=n(E)n(S)=27


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