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Question
A year is selected at random. What is the probability that it is a leap year which contains 53 Sundays
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Solution
Probability of year being a leap year = `1/4`
Probability of year being non – leap year = `3/4`
A leap year has 366 days
`366/7` = 52 weeks + 2 days
In 52 weeks,
we get 52 Sundays.
From the remaining two days we should get one Sunday
The remaining two days can be any one of the following combinations.
Saturday and Sunday, Sunday and Monday, Monday and Tuesday, Tuesday and Wednes¬day, Wednesday and Thursday, Thursday and Friday, Friday and Saturday of the seven combinations two have Sundays.
∴ (Probability of getting a Sunday = `2/7`
Selecting a leap year = `1/4`
∴ In every four consecutive years we get one leap year
∴ Probability of getting 53 Sundays = `2/7 xx 1/4 xx 1/14`
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