All the details are at Mersenne Prime Search 10. If a class has 23 students in it then the probability that at least two of the students share a birthday is about 0.5. If there are 50 students in a class then it's virtually certain that two will share the same birthday. This seems to go against common sense but is absolutely correct. For a good explanation and simulation see The Birthday Problem .
Probability can catch even the best mathematicians out.
A fair amount of controversy was created in 1990 by The Monty Hall Problem also known as The Goat and the Car .