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