# 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?

• I don't understand. Are you simply asking what is the probability that no two family members share a birthday? Or that no two family members share a birthmonth? If the former, why do you specify months? – Xander Henderson Dec 19 '17 at 1:03
• Hard to follow. what does the $30$ have to do with anything? Order them (by age, say). The probability that the first two have different birthmonths is $\frac {11}{12}$. The probability that the third has yet a different birthmonth is then $\frac {10}{12}, and$\frac 9{12}\$ for the fourth. Thus.... – lulu Dec 19 '17 at 1:27