It is surprising (but true) that if 23 randomly selected people are in the same room, there is about a 50% chance that at least two people will have the same birthday. Suppose you want to estimate the probability that if 30 people are in the same room, at least two of them will have the same birthday.
Perform the following and respond to the questions:
(A) Generate the "birthdays" of 30 different people, assuming that each person has a 1/365 chance of having a given birthday (call the days of the year 1, 2, 3, ........,365). You can use a formula involving the DISCRETE and RAND functions to generate birthdays.(B) Once you have generated 30 people's birthdays, you can tell whether at least two people have the same birthday using Excel's RANK function (i.e., in the case of a tie, two numbers are given the same rank). Do you see any people with the same birthday in your sample?
(C) Obtain at least 20 samples of the 30-person group using the F9 key. What do you estimate the probability of finding two people with the same birthday in a sample of 30 people to be?
We have to use excel to solve this question.
Can you solve this and give step by step explanations as well.