Odds of No October Birthdays in Group of 43

[ccj]

What are the odds that no one in my group has an October birthday? There are 43 people in the group.

 

[HallsofIvy]

October has 31 days and there are 365 days in a year (ignoring leap years) so the probability that a specific person does NOT have an october birthday is (365- 31)/365= 334/365. The probability that, of 43 people, NONE has an october birthday is $(334/365)^{43}$. The probabilty that at least one person of 43 has an october birthday is 1 minus that: \(\displaystyle 1- (335/365)^{43}\).

If you want to include leap years do that for four year cycles. In four years, there are 3(365)+ 366= 1461 days and there are 4(31)= 124 october days and so 1461- 124= 1337 non-october days. The probability that at least one person of 43 has an october birthday is $1- (1337/1461)^{43}$.

 

[ccj]

I really appreciate your complete answer. Thanks!

 

[ccj]

I am tryng to put the answer into a statement like " The odds of no one having an October birthday is 1 in XXX,XXXX,XXXX" When I do (attempt to do)the calc you have above, I get a .97799... number. Obviously stats was not a strenght of mine when I was in college (25 years ago) thanks and sorry for the additional qetion.

 

[DyslexicHobo]

So what you have is one fraction that you want to turn into another:

The percentage you calculated (correctly), .97799, can also be written as a fraction: .97799 / 1. A way to add meaning to this fraction is to say "The odds of at least one person having an October birthday is .97799 in 1."

From what I understand, you want the opposite of this: the odds of someone NOT having a birthday in October. To do this, use the number you first calculated, .02200. A way to give meaning to this number is by saying "The odds that no one in my group has an October birthday is .022 in 1." If you wanted to convey the same statistic by saying "The odds... is 1 in X", we can do that easily by cross-multiplication of two fractions. We can set up a proportion: .022 / 1 = 1 / X. From this, we can arrive at the equation .022*x = 1. When we divide 1 by .022, we find that the answer for X is about 45.5.

So for the final answer we arrive at the statement: "The chances that no one in the group of 43 people has an October birthday is approximately 1 in 45.5"

Hope this helps, let me know if you need clarification.

 

[ccj]

Thanks for the explanation. Stats can be fun and frustrating - for me mostly frustrating :(