Hello All,

I'm working on something that could prove very interesting. I know about the Birthday Paradox (23 or more people and you are very likely to get the same month and day). But I was wondering something and hoped you good folks could give me the odds or chances as well as the math behind all to follow:

What are the chances that a coin in someone's pocket has the same year minted on the coin as the person's Birthday year? (In USA coinage).

In other words how likely am I to get a hit for Coin's Date = Person's Birthday Year?

Thank you.

Sincerely,
Dale A. Hildebrandt

To calculate that you'd need to know the distribution of coins in circulation by year, and that distribution will change every year. There will obviously be a greater percentage of recently minted coins than older coins, so the younger the spectator the more likely it is that one of the coins in their pocket was minted in the year of their birth. I doubt that you can get much more specific than that.

Good answer!

Mike

In addition, I am finding folks are carrying fewer and fewer coins nowadays and that is happening with bills also. I carry any money I need for an effect with me because of this situation. Unfortunately that doesn't help your idea.

John

If you have a copy of (the hard to come by) Pure Effect by Derren Brown you'll find an interesting effect which utilises the occurrence of dates on circulated coins; the effect is also detailed on his DVD for International Magic (both were released just as he was first appearing on TV, and well before he became a household name in the UK).

The effect itself is sadly no longer all that applicable, and if it were was perculiar to the British mint... so irrelevant to your specific request. However, it seemed worthy of a mention here due to the similarity in nature!

All the best

Owen

Thanks for the replies so far everyone. Now, for a similar question.

I have a fishbowl containing three of each coin from the years 1965 to 1990. Is it possible to calculate how likely I would be to get a hit on having a coin selected from the fishbowl match the birth year of an audience member? Thanks in advance.

Sincerely,
Dale A. Hildebrandt

1/26; as long as you have an identical number of coins of each date and the spectator's birthyear is in the range. You get the same probability even if there is only one of each date.

/Tomas

That's correct as the probability for one individual. As the audience size increases the probability will increase. I think that's what the OP was referring to. If there are 26 people in the audience all born in a different year in the range then the probability is 1.00 (certainty).

You can't calculate the actual probabilities for a group without knowing how many audience members there are and what range of birth years they have.

If you have an audience of 100 old age pensioners then the probability is zero.

Mike

I see, I thought "an audience member" was a specific one on stage picking a coin at random. Dale, do you ask if a coin picked will match at least one audience member's birthyear? That's harder; see the post above.

/Tomas

Thanks Tomas and Mike.

Yes, Tomas, I am asking if a coin picked will match at least one audience member's birthyear. Thanks.

Sincerely,
Dale A. Hildebrandt