A simulation of a procedure is a process that behaves the same way as the proced

Question

A simulation of a procedure is a process that behaves the same way as the procedure, so that similar results are produced.

Complete the "Technology Project" at the end of Chapter 4 (pages 181-182). You will organize each group of 50 values in columns. Be sure that your use "Paste Values" to create your additional groups of 50.

In your columns, highlight any groups of 2 that share a birthday in yellow. Highlight any groups of 3 or more that share a birthday in green.

Once you have done this, open a second worksheet and repeat the process for groups of 100 people.

Explanation / Answer

One approach to solve this is to find the probability that no one has the same birthday, then subtract that from 1.

So the first person can have any of the 365 (presuming no leap years) days as a birthday, so: 365/365 = 1
the second person can have any of the remaining 364 days: 364/365
the third person can have any of the remaining 363 days: 363/365

this pattern continues for 25 people, so you have:

[365! / (365 - 25)! ] / 365^25
[365! / 340! ] / 365^25
(4.92154 * 10^63) / (1.14109 * 10^64)
(4.92154/1.14109) * (10^63/10^64)
4.31302 / 10
0.431302

That is the probability of no one having the same birthday. so the probability of at least one set of people having the same birthday will be that value subtracted from 1:

1 - 0.4313 = 0.5687 Answer

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