If a leap year is selected at random, what is the change that it will contain $53$ Tuesdays ?

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In a leap year, there are $366$ days i.e., $52$ weeks and $2$ days.

In $52$ weeks, there are $52$ Tuesdays.

Therefore, the probability that the leap year will contain $53$ Tuesday is equal to the probability that the remaining $2$ days will be Tuesdays.

The remaining $2$ days can be

Monday and Tuesday

Tuesday and Wednesday

Wednesday and Thursday

Thursday and Friday

Friday and Saturday

Saturday and Sunday

Sunday and Monday

Total number of cases $=7$

Favorable cases $=2$

Probability that a leap year will have $53$ Tuesdays $=\frac{2}{7}$

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