Question:
If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays?
Solution:
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 Tuesdays 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
Favourable cases = 2
$\therefore$ Probability that a leap year will have 53 Tuesdays $=\frac{2}{7}$
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