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- Thread starter ZZ Specs
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On this forum, we try to help folks learn how to solve problems. We don't spoon feed answers.

And by the way, this is a homework type problem so you are supposed to use the homework template. Please read the forum rules.

- #3

Chronos

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Keep in mind that it makes a difference if you are looking for exactly 3 of 5, or at least 3 of 5.

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Keep this in mind, it does in deed make a difference!Keep in mind that it makes a difference if you are looking for exactly 3 of 5, or at least 3 of 5.

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I can work it out on a tree, for instance:

19/40*(..conditional probabilities..) + 21/40*(conditional probabilities)

with 5 separate columns (if that makes sense) but I know there has to be a better way.

I understand how basic combinations could give us the chances of pulling 3 red marbles in 3 draws (i.e. all red, or all blue) but I get really messed up when I try to think about 3 red marbles out of 5 draws out of 40 marbles.

It's been a while since I did statistics haha, some hints would be nice! :D And sorry about the homework template / improper forum section, it's also been a bit since I've come to PF. No excuse, of course, totally my fault. I can re-post in the homework section if it's an issue.

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Does that not ignore certain conditions of non-repetition though? Once you draw the first marble, the probabilities of the next draw have already changed.

I believe it is correct that there are 5! = 120 ways of picking 3 red and 2 blue marbles, if that is anywhere near where you are getting at. Thanks for your help so far!

- #8

HallsofIvy

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The probability the first marble you pick is red is, of course, 19/40. Now there are 39 marbles left and 18 are red. The probability that the second marble is red is 18/39. Now there are 38 marbles left and 17 are red. The probability that the third marble is red is 17/38. Now there are 37 marbles left and 21 of them are blue. The probability the fourth marble is blue is 21/37. There are now 36 marbles left and 20 of them are blue. The probability the fifth marble is blue is 20/36.

That will give you the probability of three red marbles

But if you calculate a different order, say RRBRB, you will see that while you get different fractions, the

But that is NOT 5!. Since all red are the same and all blue marbles are the same, the number of different orders is

[tex]_5C_3= \begin{pmatrix}5 \\ 3\end{pmatrix}= \frac{5!}{3!2!}= \frac{5(4)}{2}= 10[/tex].

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