What is the probability that an ordinary year has 53 Tuesdays?

Question:
What is the probability that an ordinary year has 53 Tuesdays?

Solution:

We know that,

Probability of occurrence of an event

$=\frac{\text { Total no.of Desired outcomes }}{\text { Total no. of outcomes }}$

An ordinary year has 365 days i.e. it has 52 weeks $+1$ day. So, there will be 52 Tuesdays for sure(because every week has 1 Tuesday)

So, we want another Tuesday that to from that 1 day left(as there is only one Tuesday left after 52 weeks)

This one day can be, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.Of these total 7 outcomes, the desired outcome is 1 , i.e. Tuesday

Therefore, the probability of getting 52 Tuesdays in an ordinary year

$=\frac{1}{7}$

Conclusion: Probability of getting 53 Tuesdays in an ordinary year is $\frac{1}{7}$

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