A few days back, I called up an old friend Anamika to wish her happy birthday and she told me that she was out having lunch with her neighbor who also has the exact same birthday!! That got me thinking about what is the probability of such a coincidence happening. Here is a puzzle from that thought process.
If you are mathematically oriented, try solving it. If not, take a guess and see how it compares with the right answer. My guess is that the guess is going to be much larger than the actual number.
Simply put, what is the minimum size of a class where the probability that there is at least one birthday that is shared by two students is more than 50%?
Put in details, if you have two students in a class, the chance they will have the exact some birthday is 1/365. If a third student comes in, there is a higher probability of two of them having the same birthday. If a fourth student comes in, the probability increases further. At what size of the class do you have a 50-50 chance of a birthday being repeated?