SOLUTION: What is the probability that there are at least two people with the same birthday in a class of 40?

Question 1118481: What is the probability that there are at least two people with the same birthday in a class of 40?
Found 2 solutions by Shin123, math_helper:
Answer by Shin123(626) (Show Source): You can put this solution on YOUR website!
The number of possible incomes is which is 1,099,511,627,776. There is 41 incomes that does not favor the probability we want to get. So 1,099,511,627,776-41=1,099,511,627,735. Therefore, the probability is which is approx. 99.9999999962711%
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
P(at least two people share a birthday) = 1 - P(no two people share a birthday)

The 1st person has some birthday...
The 2nd person has 364 possible non-matching birthdays�
That leaves 363 non-matching birthdays for the 3rd person
etc.

Extending this to 40 people:
P(no two people share a birthday) = * � * = 0.1088

P(two or more people share a birthday) = 1 - 0.1088 =

So in a class of 40, it is far more likely that two or more people share the same birthday than for no two people to share a birthday. [ It only takes 23 people to reach a probability of >50% that two people will share the same birthday ]. If this seem nonintuitive, note that the above gives the probability that ANY two people share a birthday. If you are in a class of 40 students, the probability that someone also has YOUR birthday is still a pretty small number (about 1/10).
��
Edit 6/11: Tutor @Shin123 has arrived at an incorrect answer, using an incorrect method.
RELATED QUESTIONS
There are 65 people in a room. What is the probability that at least two have the same... (answered by Boreal,solver91311)
There are 30 people in a room. What is the probability that at least two of these people... (answered by ewatrrr)
What is the probability that out of a group of five people, at least two people have the... (answered by VFBundy)
assume there are 365 days in a year, from a group of 4 random people a) what is the... (answered by ikleyn)
In a room full of 30 people, what is the probability that at least two people have the... (answered by Edwin McCravy)
I'd appreciate some help with this problem. It is too complex for me to even begin to... (answered by stanbon)
In a room full of 30 people, what is the probability that at least two people have the... (answered by vleith)
Assuming there are 365 different birthdays, find the probability that of three people... (answered by solver91311)
if three people are randomly selected, what is the probability at least two of them have... (answered by edjones)