The birthday paradox is that there is a surprisingly high probability that two people in the same room happen to share the same birthday. By birthday, we mean the same day of the year (ignoring leap years), but not the exact birthday including the birth year or time of day. Write a program that approximates the probability that two people in the same room have the same birthday, for 2 to 50 people in the room.

The program should use simulation to approximate the answer. Over many trials (say, 5000), randomly assign birthdays to everyone in the room. Count up the number of times at least two people have the same birthday, and then divide by the number of trials to get an estimated probability that two people share the same birthday for a given room size.

Your output should look something like the following. It will not be exactly the same due to the random numbers:

For 2 people, the probability of two birthdays is about 0.002

For 3 people, the probability of two birthdays is about 0.0082

For 4 people, the probability of two birthdays is about 0.0163

. . .

For 49 people, the probability of two birthdays is about 0.9654

For 50 people, the probability of two birthdays is about 0.969.