double trouble

[topaz]

Morgan's homework today included this problem (reproduced here verbatim):

If you have one dice with the numbers 1, 2, 3, 4, 5, and 6. Expressed as a fraction, what is the probability of rolling a double (2 of the same number) in 25 rolls?

The probability that at least one number will come up twice is clearly 100%.  We're assuming that they're asking for the probability that at some point two consecutive rolls will turn up the same number.

This seems like a remarkably sophisticated problem to assign a sixth-grader.  It looks like it would have been a reasonable problem for my probability midterm in high school.  Does anyone here disagree?

Edit: The problem was not made up or handwritten by the math teacher -- it was submitted as part of a Math 4 Today handout that he gets assigned on a weekly basis.  For better or for worse, this was part of a standard curriculum math workbook.  (And they wonder is our children learning anything!)

Comments

[matthewwdaly.livejournal.com]

I'm confused by "one dice". If they meant "one die", then you're probably right. I'm wondering if they didn't mean "one pair of dice", which would be a slightly more intuitive problem. I don't think either is a killer as long as you've been taught the addition and multiplication rules for probability.

Still, holy cow. I'm not sure I knew what abstract exponentiation was in sixth grade, and certainly not that numbers as high as 6^25 could be arithmetically processed, and I was a prodigy.

(Sorry for the drive-by.)

[qwrrty.livejournal.com]

Hey, no worries. You're right, if they meant "a pair of dice" by "one dice" then that simplifies the problem a lot. I don't think any of us even considered that interpretation.

[matthewwdaly.livejournal.com]

Your interpretation isn't too rough. For each of the rolls after the first one, the probability of matching the previous roll is 1/6, so the probability that it happens at least once is 1-(5/6)^24. It's a subtle argument that those events are all independent, though, and I'd hate to set a sixth-grader down the path of never thinking about the risk of dependency contaminating the probabilities.

[razil.livejournal.com]

Yes. My first reaction is "0" since if you only have one die you obviously can't roll a double. :)

[buddhagrrl.livejournal.com]

In all seriousness, that was my first reaction too, and I assumed the problem was just incorrectly worded.

[dancingwolfgrrl.livejournal.com]

Me three, although I meant it snarkily, assuming that "one dice" was intended to mean "one pair of dice" and that since they can't type, I am not required to do any math.

[spike.livejournal.com]

I disagree. The standard 'pip pattern' for six is clearly a double-three:

o   o
o   o
o   o

The pip pattern for four is less clearly, but still arguably a double-two. The pip pattern for two is only barely arguably a double-one.

[blk]

I bet this is right, and they meant "a pair of dice." That makes the next sentence make much more sense.