In a class of 30, what is the probability that 2 people have the same birthday?
To find the probability that two people in a class of 30 have the same birthday, we can use the concept of the birthday problem.
The calculation involves calculating the probability that none of the 30 people share the same birthday, and then subtracting that from 1 to get the probability that at least two people share the same birthday.
To start, let's calculate the probability that the first person does not share their birthday with anyone else. The probability for the first person is simply 365/365, as they can choose any day without restriction.
For the second person, the probability that they do not share their birthday with the first person is 364/365, as there are 364 remaining days available.
For the third person, the probability that they do not share their birthday with either the first or second person is 363/365.
We continue this pattern until the 30th person. The probability that all 30 people have different birthdays can be found by multiplying each of these probabilities together:
(365/365) * (364/365) * (363/365) * ... * (336/365)
Now, to find the probability that at least two people share the same birthday, we subtract the probability that all 30 people have different birthdays from 1. So the final probability would be:
1 - ((365/365) * (364/365) * (363/365) * ... * (336/365))
Evaluating this expression will give us the probability that two people in a class of 30 share the same birthday.