I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!

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?

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).

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...)

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I found two possible answers.

ReplyDelete90%...

pennies 45

nickels 2

dimes 2

quarters 1

or

80%...

pennies 40

nickels 8

dimes 2

quarters 0

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

ReplyDeleteThere 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).

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...)

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

ReplyDeleteI 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.