I must say BelleMa, it's great to see you delving into the magical world of statistics... I can vouch for your claim regarding birthdays and the probability of several of them having the same birthday. Here's the equation for this particular problem:

The Probability that NO two people in a group have the same birthday is as follows:

365!/[(365-n)!365^n] Where n= the number of people in the sample group.

For this example, when using n=23, our final answer is 0.4927, or as a percentage, 49.27%. This answer tells us that there is a 49.27% probability in a group of 23 people, that NO two people share a birthday. Therefore we can subtract our answer from 1 to get the answer we're looking for...

1-0.4927=0.5073

This tells us as you stated in your post, that in a group of 23 people, there is a 50.73% probability that at least two people share a birthday.

Considering that both Megs and I share the same birthday, using this same equation to determine the probability of any two people sharing the same birthday, we had a (1-0.9973=0.0027) or 0.27% probability of sharing a birthday.

## 3 comments:

Happy Birthday, Jantzen!

I must say BelleMa, it's great to see you delving into the magical world of statistics... I can vouch for your claim regarding birthdays and the probability of several of them having the same birthday. Here's the equation for this particular problem:

The Probability that NO two people in a group have the same birthday is as follows:

365!/[(365-n)!365^n]

Where n= the number of people in the sample group.

For this example, when using n=23, our final answer is 0.4927, or as a percentage, 49.27%. This answer tells us that there is a 49.27% probability in a group of 23 people, that NO two people share a birthday. Therefore we can subtract our answer from 1 to get the answer we're looking for...

1-0.4927=0.5073

This tells us as you stated in your post, that in a group of 23 people, there is a 50.73% probability that at least two people share a birthday.

Considering that both Megs and I share the same birthday, using this same equation to determine the probability of any two people sharing the same birthday, we had a (1-0.9973=0.0027) or 0.27% probability of sharing a birthday.

Oh the magic of statistics.

I usually defer to Dilbert's method of statistical analysis...much easier to compute.

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