Question
Tue August 14, 2012 By: Nilesh Raikar
 

find the probability of having a. 5 monday in the month of january i)in a leap year ii)in a nonLeap year. b. 5 monday in the month of february i)in a leap year ii)in a nonLeap year.

Expert Reply
Sat August 18, 2012
a. In January you have 31 days (regardless of leap year). That would be 4 weeks and 3 days. So you'd need one of those 3 extra days to be a Monday. That would happen nominally 3/7 of the time.

b. In a leap year, February has 29 days. In order to get 5 Mondays in a 29-day month, the first day of the month must be a Monday.
The probability that a given day is a Monday is 1/7. Hence, the required probability is 1/7.

In a non-leap year, February has 28 days. So each day occurs exactly 4 times. So the probability of having 5 Mondays is Zero.
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