Birthday Problem: Months and Dates should be taken into consideration In a family of four, what is the probability that no two people have the same birthdays in the same month.(Assuming that all the months have equal probability)
Firstly I understood the question to be similar to the one that asks for the probability of no two people having the sam birthdate. 
So I tried that P(of no two people sharing the same Bday in same month)= 1-P( two people have the same Bday)
1-4C2/30 (Assuming that every month has 30 days. =1-0.2 =0.8.
Am I on the right track?
 A: As Xander Henderson said, if the question is just 'what is the probability that two people have the same birthday' then individual months is not relevant- though the year, whether a leap year or not, can.  
There are 365 days in a non-leap year.  Person "A" has some birthday.  In order that person "B" has the same birthday, his birthday must be that 1 day out of 365.  The probability of that is 1/365.
There are 365 days in a leap year.  Person "A" has some birthday.  In order that person "B" has the same birthday, his birthday must be that 1 day out of 366.  The probability of that is 1/366.
To get the "overall" probability, use the fact that 1/4 of all years are leap years, 3/4 are not*.  So the probability two people share the same birthday is (3/4)(1/365)+ (1/4)(1/366).


*

*Strictly speaking, this is not exactly true.  In the Gregorian calendar, Any year divisible by 100 but not divisible by 400, is NOT a leap year.  1800 and 1900, though divisible by 4 were not leap years because they are divisible by 100.  The year 2000 was a leap year. It is divisible by 100 but also by 400. 

