At a party, often there is a pair(s) whose birthday is the same. If the attendees are 23 or more, the chance for such a pair is over 50%.

Let's calculate the probability of having at least one pair. Calculating this probability directly is quite tricky, so here we calculate the possibility of "having no pairs" whose birthday is the same.
By calculating "having no pairs" and subtracting this from 1, you will get "having at least one pair".

Suppose the member is two. The "having no pairs" is 364/365. If the second person's birthday is not the first person's, then "having no pairs".

Suppose the member is three. The "having no pairs" is (364/365) * (363/365). If the second person's birthday is not the first person's, and the third person's birthday is not either the first person's or the second person's,  then "having no pairs".

For more members, multiply by (x/365) where x decreases by -1.

Having a pair probability:
(cf.)The probability that you find a person of the same birthday:

Is there a pair for having the same birthday in people?

Simulation results will be displayed here.

#### Do you think the probability is strange?

If the member is 23 or more, the probability of having such a pair is over 50%. You might think this probability is too high.
Maybe, you might confuse these two;

• The probability that you find a person whose birthday is the same as you.
• The probability that at least one person finds a person whose birthday is the same as him/her.

The probability that you find a person whose birthday is the same as you, will be
1- (364/365 * 364/365 * 364/365 * ...)

This probability is substantially low.

*In this calculation, we ignore February 29th.

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