Question

What is the probability that a leap year has 53 Tuesdays and 53 Mondays?

Answer 1

Hint: Here the leap year has 366 days which has 52 weeks and 2 days.Write all the possibilities which satisfies the condition for 2 days i.e.Monday and tuesday.Then we have to find the total sample space.Divide the favourable sample space with total sample space to get the required probability.

Complete step-by-step answer:
A leap year has 366 days. Now the closest number divisible by 7 is 364, therefore there will be 2 excess weekdays in a leap year.
The 2 excess weekdays can be (Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday). So, the sample space S has 7 pairs of excess weekdays, i.e.
\[n(S) = 7\]
Now we want the desired event E to have 53 Mondays and 53 Tuesdays. E consists of only one pair in S which is (Monday, Tuesday)
\[n(E) = 1\]
Hence the probability that a leap year will contain 53 Mondays and 53 Tuesdays is
\[P = \dfrac{{favorable{\text{ }}sample{\text{ }}space}}{{total{\text{ }}sample{\text{ }}space}} = \dfrac{{n(S)}}{{n(E)}} = \dfrac{1}{7}\]
So, this is your required possibility.

Note: In this type of questions first calculate the total sample space, then calculate the favorable sample,students should take care while writing favourable sample space, lot of mistakes will do here only So,according to the given condition, have to take it.Divide the favourable sample space with total sample space to get the required probability.