We have the same birthday! What are the chances of that?

No it’s not my birthday.

Some random neuron fired on brain today and I recalled an item in one of Martin Gardner’s books:
How many people do you need to ensure that two of them will have a better than 50-50 chance of have the same birthday (day and month)?

Since most people, including me, have a poor grasp of probability (hence the success of the lottery and the idea of synchronicity) the reply is usually: “Lots”.

The answer is 24.

The probability that two people will have different birthdays is 364/365.

The probability that a third person will have a birthday different from the other two is 363/365.

For a fourth person the probability is 362/365 and so on, continuing to the 24th person who has a probability of 342/365.

This gives us 24 fractions which when multiplied together gives the probability that all 24 birthdays are different: 23/50.

So the next time you are in a gathering of 24 people or more, there is a better than 50/50 chance that two of them will have the same birthday. And probably did not realise it.

By one of those strange quirks of the cosmos, 24 is the number of people who have travelled to the Moon, from Apollo 8 – 17.  We find that Eugene Cernan and Frank Borman were both born on March 14th. Furthermore Ken Mattingly and James Irwin were born on March 17th, and Edgar Mitchell and Tom Stafford were born on November 17th.

Birth dates were obtained from the List of Apollo astronauts at Wikipedia

[This is a rephrasing of how the paradox is posed in the book “Mathematical Puzzles and Diversions”, Martin Gardner. Pelican books 1959. And Gardner is referencing an earlier book by George Gamow “One, Two, Three – Infiinity”].

A short curiosity about aliens is here…….

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