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

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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):
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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).
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Edit 6/11: Tutor @Shin123 has arrived at an incorrect answer, using an incorrect method.