Question

In a group of 51 people, what is the probability that at least two people share...

In a group of 51 people, what is the probability that at least two people share the same birthday? What about three people? Use Excel random number generator and a sufficient number of loop iterations to solve.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Load the data into Excel.

Use the function =RANDBETWEEN(1,365).

You have to limit your range from 1 to 365 so that you can check which day is common for the people.

Now, since they are random numbers, your random numbers generated from Excel can be different from mine.

The random numbers obtained from Excel are:

Birthday
158
278
141
333
254
288
175
244
81
252
7
332
70
225
312
207
86
359
126
284
264
90
169
98
134
104
135
277
78
16
104
203
232
337
243
363
295
338
233
12
283
140
178
77
162
245
225
106
135
135
333

The formula used is:

Birthday
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)
=RANDBETWEEN(1,365)

What is the probability that at least two people share the same birthday?

From the above data, we can see that:

Birthday Frequency
333 2
225 2
104 2
Birthday Frequency
135 3

Therefore, the probability that at least two people share the same birthday will be:

= 2+2+2+3/51 = 9/51 = 0.176471

What about three people?

The probability that three people share the same birthday will be:

= 3/51 = 0.058824

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