Probability help

[tahnan]

It's been a long time since I've done probability, and I'd love for someone to check my work on the following question:

Suppose you have 58 marbles in a jar, 28 white and 30 black, and you draw a marbles from the jar without replacement.

(a) If you draw 19 total, what's the probability that exactly 9 will be black?
(b) If you draw 17 total, what's the probability that all 17 will be black?

If I've done this right, I get 19.8% for the first one and .00006% for the second, using the calculations (28-choose-10)*(30-choose-9)/(58-choose-19) and (30-choose-17)/(58-choose-17) and relying on Python to do the actual arithmetic.

Comments

[touchstone.livejournal.com]

I've forgotten most of my probability, but I did B the 'long way' just to check, since it was simple, and can confirm 0.00006%.

[luckylefty.livejournal.com]

Haven't checked the arithmetic, but I got the same combination-expressions for the answer that you did.

[rikchik.livejournal.com]

B is much easier and I can confirm your results. A I'm not sure about - do you have to account for getting the black and white marbles interleaved?

And do these problems correspond to anything? The numbers are kind of strange to have been picked as just an exercise.

[tahnan.livejournal.com]

For A, order of marbles doesn't matter.

And yes, they do correspond to something, though I can't really discuss the details here.

[mickeymao.livejournal.com]

I also get the same result for B, and am over my head when it comes to A.

[acroarcs.livejournal.com]

I can confirm both, as well as the approach to do both. I always have a hard time approaching problems like A, so I rederive from first principles each time - but that's the calculation I get to from there. It's longer, but I'm more sure of it.

[tahnan.livejournal.com]

Excellent--thanks!

[devjoe.livejournal.com]

Yes, this is what I got and how I got it.

For (a), 58-choose-19 represents the total number of ways to choose 19 marbles out of 58, ignoring the order of choosing them. Then 28-choose-10 represents the number of ways to choose 10 white marbles, and 30-choose-9 represents the number of ways to choose 9 black marbles, and their product is the number of ways to choose 10 white and 9 black marbles, and finally you divide these two results to get the probability. Then (b) is the same sort of calculation except there are no white ones being chosen, so the white term becomes 28-choose-0 which is 1 and drops out of the product.

[jydog1.livejournal.com]

I like marbles!

That's all you're gettin' from the English major.

[tahnan.livejournal.com]

Then why did you lose all of yours?

[thatwesguy.livejournal.com]

(28-choose-10)*(30-choose-9)/(58-choose-19) and (30-choose-17)/(58-choose-17) are correct, respectively.

In general, the odds of doing something you want is equal to the number of ways you can do the thing you want, divided by the number of ways you can do anything at all (assuming that all outcomes are equally likely), and that's exactly what you've done here.

(And if not, then I charge waaaaay too much money for test prep. ;-) )