math
posted by Kimberly .
Find the probability of at least one birthday match among a group of 48 people.

The probability is
1  Probability of no matches
The probability of no matches is the ratio of the number of ways you can choose the birthdays such that each person has a different birthday (let's call this N) divided by the number of ways to distribute birthdays without restriction (let's call this M).
CLearly M = 365^48
and
N = 365!/(365  48)!
To see this, consider that the first person can have 365 birhtdays, the second can have 3651 as his/her birthday bust be different from the first, The third can have 365  2 birthdays, etc. etc.
Then, to evaluate the numbers you have to be careful if your calculator does not display numbers larger than 10^100. You can then take logarithms and use Strirling's formula to evaluate the factorials, or simply sum the 48 terms in the expression for Log(N).
Yo should fiund that 1  N/M = 0.9606
Respond to this Question
Similar Questions

math
the smallest number of people in a room where the probability of two of them having the same birthday is at least 50 percent. Answer is between 1 and 31. This is a classic problem given in probability classes. There are plenty of sites … 
math
the smallest number of people in a room where the probability of two of them having the same birthday is at least fifty percent Please post under one name. The smallest class where the chance of finding two people with the same birthday … 
Math
What is the probability that at least 2 people in a random group of 4 people have a birthday on the same day of the week? 
STATISTICS
From a group of 12 people, you randomly select 3 of them. Find the probability that at least one of them is among the 3 oldest people in the group 
STATISTICS
From a group of 12 people, you randomly select 3 of them. Find the probability that at least one of them is among the 3 oldest people in the group 
Math Prob Stat
The probability that a student in this school has a job is 65%. What is the probability that: A. You ask at least 8 people before you find someone with a job? 
Statistics
A youth group has 7 boys and 5 girls. Experiment is select 5 people at random from the group. Let X be the number of boys in the selected 5 people. (a) Find the probability of exactly 1 boy, i.e., P([X = 1]). (b) Find the probability … 
Probability Help
Forty people are selected at random. What is the probability that none of the people in this group have the same birthday? 
Probability Help
Forty people are selected at random. What is the probability that none of the people in this group have the same birthday? 
Probability Help
Fourty people are selected at random. What is the probability that none of the people in this group have the same birthday?