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.
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) |
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| =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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