What is the probablity of January having 5 sundays. Similarly for the other months I'm trying to find out what is the probability that a randomly chosen January will have 5 Sundays. Of course the answer for 4 Sundays would be 1. I presume that 31 day months will have a higher probability of having 5 then 30 day months. Of course, February in a non-leap year has 0 probablity of having 5 sundays and in a leap year will have 5 only if 1st Feb is a Sunday. Therefore in a leap year P(Feb,5) = 1/7 and over a 400 year time period the P(Feb,5) will be 99/2800. I presume all 31 day months will have the same probablity which should be higher than 30 day months and in turn will be higher than 99/2800. I've worked out P(31d month,5) will be 223/343 and P(30d month,5) is 19/49. Is this right?
 A: You have to be a little careful calculating this. With the leap year rules the calendar repeats after 400 years (the number of days in 400 years is divisible by $7$). In any period of 400 years using the current calendar, 1 January will fall on:
Sunday 58 times
Monday 56 times
Tuesday 58 times
Wednesday 57 times
Thursday 57 times
Friday 58 times
Saturday 56 times
A: January will have 5 Sundays if January 1 falls on Friday,  Saturday or Sunday. Therefore the probability is 3/7. You can apply the same logic for other months.
A: now it is sure that the month of jan will have 4 sundays as you said. so 31-28=3 days remaining
the remaining 3 days can have different combination of days
sun-mon-tue
mon-tue-wed
tue-wed-thu
wed-thu-fri
thu-fri-sat
fri-sat-sun
sat-sun-mon
so there are total 7 combinations
and 3 of these combinations contains sunday
so probability of having 5 sundays in the month of january is P(E)= 3/7
A: 3 by 7 is the perfect answer.as there are seven days in a week and there are 3 possible outcomes 
Possible outcomes ÷ total number of favourable outcomes.
