Determination of Probabilities through Symmetry Considerations
There are n students in a classroom. What is the probability for the fact that at least two of them have their birthday on the same day? Solve the problem by working through the following questions:
(a) What is the number N of possibilities to distribute the n birthdays over the year (365 days)?
(b) How large is the number N' of possibilities for which all n birthdays are different?
(c) How large then is the probability Pdiff that the birthdays are different?
(d) How large finally is the probability P that at least two birthdays are not different?