Stats Made Easy

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Sunday, April 12, 2009

TV detectives stumble over odds of matching birthdays

Ever since his glory days as the laid-back Hawaiian detective “Magnum PI” I’ve always been a fan of actor Tom Selleck. Now he’s back on television as a moody police chief named Jesse Stone – a character based on a series of mystery novels written by Robert Parker. In the latest installment of the TV franchise (the first one not based directly on one of Parker’s books) Stone searches for a stolen baby thought to be living with the thief in his small Massachusetts’ town. All they know is the birthday and approximate age. One child comes up as a match, but the deputy cautions that it only takes 22 people to get two with the same birthday.

This birthday paradox provides some fun for teachers of statistics who have large enough classes to make a match likely: Simulate the possible outcomes with this fun applet by Stanford Professor Susan Holmes. However, the odds of matching an exact birthday are far lower – it takes 252 to achieve a 50% probability. These statistics are detailed by this Wikipedia article -- see the graphical comparison of the cumulative probabilities.

So I think the odds were fairly high that Chief Stone's hunch about the baby-snatcher was a good one -- simply based on the birthday of the child being a match. In any case, amazing coincidences are standard for novels, movies and television. The writers operate in a world where chance takes a back seat to drama. Thank goodness for that -- real statistics tend to be a bit boring for entertainment purposes.

PS. The photo is one of my all-time favorites from the family album -- it's my son Hank, who helps me with this blog. The Anderson clan now is up to 9 counting those who've married in. So far none of us share a birthday.


  • At 8:59 AM, Anonymous Anonymous said…

    Here's the advanced birthday problem.

    What is the expected number of people needed to cover all 366 possible birthdays?

    If you can assume a uniform distribution of birthdays the problem isn't too bad. But is uniform assumption valid?

    Birthday's not uniform


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