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Exercise
The birthday paradox is that there is a surprisingly high probability that two or more 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 that includes the birth year or time of day. Write a program that approximates the probability that 2 or more 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, 5,000), randomly assign birthdays (i.e., a number from 1–365) to everyone in the room. Use a HashSet to store the birthdays. As the birthdays are randomly generated, use the contains method of a HashSet to see if someone with the same birthday is already in the room. If so, increment a counter that tracks how many times at least two people have the same birthday and then move on to the next trial. After the trials are over, divide the counter by the number of trials to get an estimated probability that two or more 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 0.002For 3 people, the probability of two birthdays is about 0.0082For 4 people, the probability of two birthdays is about 0.0163For 49 people, the probability of two birthdays is about 0.9654For 50 people, the probability of two birthdays is about 0.969
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