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?
[Math] the probablity of January having 5 sundays. Similarly for the other months
calendar-computationsprobability
Best Answer
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