Wednesday, August 23, 2006

Spare change?

Mary had a coin purse with fifty coins, totaling exactly $1.00. Unfortunately, while counting her change, she dropped one coin. What is the probability that it was a penny?


  1. I found two possible answers.
    pennies 45
    nickels 2
    dimes 2
    quarters 1

    pennies 40
    nickels 8
    dimes 2
    quarters 0

  2. Nice job, George. Put them together and you get an 85% probability.

    There are two (and only two) combinations of 50 coins that will add up to $1.00. These are:

    40 Pennies, 2 Dimes, 8 Nickels, and
    45 Pennies, 2 Dimes, 2 Nickels, 1 Quarter

    In the first combination there is an 80% probability, and the second gives you 90% probability. But because we don't know which she had, the probability is the average of the two, or 85%. (i.e. either combination is equally likely).

  3. I would argue if she's got so many coins, likely as change from other transactions, then there's a higher likelihood she'd have a quarter. This is based on typical marketplace pricing tactics. So I'd say the likelihood that any one coin is a penny is clsoer to 80% than 90%. (Obviously, my argument is based on a different kind of stats...)

  4. Yes, you could apply Bayes rules to this, but I'm not sure I follow your logic.

    I almost always use up my quarters, but I usually end up with a ton of pennies lying around.

    But I also tend to end up with very few nickels. So, I would tend to lean towards the 90%, given only 2 nickels vs 8 nickels.


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