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!
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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.