What is the probability that a leap year has 53 Sundays?

1.	What is the probability that a leap year has 53 Sundays?
Answer» We know that, Probability of occurrence of an event = \(\frac{Total\,no.of\,Desired\,outcomes}{Total\,no.of\,outcomes}\) A leap has 366 days i.e. 52 weeks + 2 days. So, there will be 52 Sundays for sure (because every week has one Sunday) So, we want another Sunday from the remaining two days. The two days may be Sunday, Monday or Monday, Tuesday or Tuesday, Wednesday or Wednesday, Thursday or Thursday, Friday or Friday, Saturday or Saturday, Sunday So, total outcomes are 7 and desired the outcomes are 2(Sunday, Monday or Saturday, Sunday) Therefore, the probability of getting 53 Sundays in a leap year \(\frac{2}{7}\) Conclusion: Probability of getting 53 Sundays in a leap year is \(\frac{2}{7}\)

Answer»

We know that,

Probability of occurrence of an event

= \(\frac{Total\,no.of\,Desired\,outcomes}{Total\,no.of\,outcomes}\)

A leap has 366 days i.e. 52 weeks + 2 days. So, there will be 52 Sundays for sure (because every week has one Sunday)

So, we want another Sunday from the remaining two days.

The two days may be Sunday, Monday or Monday, Tuesday or Tuesday, Wednesday or Wednesday, Thursday or Thursday, Friday or Friday, Saturday or Saturday, Sunday

So, total outcomes are 7 and desired the outcomes are 2(Sunday, Monday or Saturday, Sunday)

Therefore, the probability of getting 53 Sundays in a leap year

\(\frac{2}{7}\)

Conclusion: Probability of getting 53 Sundays in a leap year is \(\frac{2}{7}\)

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