Is anyone good at probability?

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A bag contains 10 red marbles, 6 green marbles, and 3 blue marbles. Ron chooses 3 marbles from the bag.

Find the probability of Ron choosing one of each color and Ron choosing exactly two green, with and without replacement.
 
Solution
sarkwalvein
1. P(r)*P(g|r)*P(b|g,r)+P(r)*P(b|r)*P(g|b,r)+
P(g)*P(r|g)*P(b|g,r)+P(g)*P(b|g)*P(r|b,g)+
P(b)*P(r|b)*P(g|b,r)+P(b)*P(g|b)*P(r|g,b)

2. P(g)*P(g|g)

With replacement: P(x|y) = P(x)
Without replacement: More work.

Well, I'm lazy but here it goes with the numbers:

(with replacement)
1. (10/19) * (6/19) * (3/19) * 6 = 15.74%
2. (6/19) * (6/19) = 9.97%

(without replacement)
1. (10/19) * (6/18) * (3/17) + (10/19) * (3/18) * (6/17) +
(6/19) * (10/18) * (3/17) + (6/19) * (3/18) * (10/17) +
(3/19) * (10/18) * (6/17) + (3/19) * (6/18) * (3/17) = 16.41%

2. (6/19) * (5/18) = 8.77%
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Lacius

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In statistics, you can multiply together the odds of individual things happening to yield the odds of multiple things happening. For example, the odds of getting heads on a flipped coin are 1/2, and tails is 1/2. The odds of getting a heads two times in a row are (1/2)*(1/2)=(1/4). You can apply this concept to your word problem.
 
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sarkwalvein

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1. P(r)*P(g|r)*P(b|g,r)+P(r)*P(b|r)*P(g|b,r)+
P(g)*P(r|g)*P(b|g,r)+P(g)*P(b|g)*P(r|b,g)+
P(b)*P(r|b)*P(g|b,r)+P(b)*P(g|b)*P(r|g,b)

2. P(g)*P(g|g)

With replacement: P(x|y) = P(x)
Without replacement: More work.

Well, I'm lazy but here it goes with the numbers:

(with replacement)
1. (10/19) * (6/19) * (3/19) * 6 = 15.74%
2. (6/19) * (6/19) = 9.97%

(without replacement)
1. (10/19) * (6/18) * (3/17) + (10/19) * (3/18) * (6/17) +
(6/19) * (10/18) * (3/17) + (6/19) * (3/18) * (10/17) +
(3/19) * (10/18) * (6/17) + (3/19) * (6/18) * (3/17) = 16.41%

2. (6/19) * (5/18) = 8.77%
 
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Solution
Bimmel

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Hm.. I just read through this on several sites to get the system.

It's basically..

the amount of best results
______________________
the amount of total results

But you example goes over the generic example I solved. Did you get any instruction from your school? Or did you solve a similar problem before that? Seems a bit advanced.
 
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