Birthday ProbabilitiesDate: 12/09/97 at 23:56:40 From: Fred Subject: Probability for people's birthdays and the days of the week and astrological signs What's the minimum number of people you need in order for the probability that two of them were born on the same day of the week to be 50 percent? And the same for the same astrological sign. If you could help me out; I'm a little unclear with probabilities and statistics and such, so any help would be greatly appreciated. Thank you. Date: 12/10/97 at 12:13:54 From: Doctor Anthony Subject: Re: Probability for people's birthdays and the days of the week and astrological signs We shall calculate the probability that no two have birthdays on the same day of the week and subtract that probability from 1 For no two to share the same day, the first person has 7 choices, the second person 6 choices the third person 5 choices and so on. If there are n persons 7 x 6 x 5 x 4 x ....(7-n+1) P(7,n) Probability = ----------------------------- = -------- 7^n 7^n The probability that at least two have birthdays on the same day of the week P(7,n) = 1 - ------- > 0.5 7^n P(7,n) So ------ < 0.5 7^n Using trial and error n = 3 P(7,3)/7^3 = 0.6122 n = 4 P(7,4)/7^4 = 0.34985 and so 4 people is sufficient to give a better than 50% chance that at least two have birthdays on the same day of the week. Since there are 12 different astrological signs (instead of 7 different days), the calculation would be P(12,n) --------- < 0.5 12^n Trial and error shows that n = 7 P(12,7)/12^7 = 0.1114 n = 5 P(12,5)/12^5 = 0.3819 n = 4 P(12,4)/12^4 = 0.5729 and so 5 people are sufficient to give a better than 50% chance that at least two have the same astrological sign -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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