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# A bag of 10 marbles contains 3 red marbles and 7 blue

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Re: A bag of 10 marbles contains 3 red marbles and 7 blue [#permalink]  07 Mar 2012, 23:02
Owsum Bunuel ... Thanks !
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Re: Combinatorics - at least, none .... [#permalink]  01 Apr 2013, 08:51
Bunuel wrote:
Bullet wrote:
Thanks Bunuel. I posted the solution from the thread as i was confused with the solution.

So what you're saying is that we need to multiply the permutations with the probability. Having said that we will do only when we need to choose at least two marbles or any other thing from the whole?

Thanks

To make it simple: suppose we have the jar of 10 marbles - 5 red, 2 blue and 3 green. If five marbles are selected at random, what is the probability that two will be red, one blue and two green?

We are looking for all the cases with 2R, 1B and 2G. We can draw these marbles like: RRBGG or GGBRR or RBGGR ... So how many combinations of the drawing of these marbles are there? The answer is as many as there is permutation of the letters GGBRR, which is \frac{5!}{2!2!}.

Hence the answer for the above question would be \frac{5!}{2!2!}*\frac{5}{10}*\frac{4}{9}*\frac{2}{8}*\frac{3}{7}*\frac{2}{6}.

If the question were: three marbles are selected at random, what is the probability that all three will be red?

RRR can occur only in one way: RRR, so the probability would be \frac{5}{10}*\frac{4}{9}*\frac{3}{8}.

You can check the Probability and Combination chapters in the Math Book (link below) for more.
Also check my posts at:
probability-colored-balls-55253.html#p637525
4-red-chips-and-2-blue-chips-85987.html#p644603
probability-qs-attention-88945.html#p671958
p-c-88431.html?highlight=probability+of+occurring+event
probability-88069.html?highlight=probability+of+occurring+event
combination-problem-princenten-review-2009-bin-4-q2-87673.html?highlight=probability+of+occurring+event

That was an awesome explanation. Thank you!
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petrifiedbutstanding

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Re: A bag of 10 marbles contains 3 red marbles and 7 blue [#permalink]  08 Feb 2014, 13:21
bmwhype2 wrote:
1. A bag of 10 marbles contains 3 red marbles and 7 blue marbles. If two marbles are selected at random, what is the probability that at least one marble is blue?

2. A bag of 10 marbles contains 3 red marbles and 7 blue marbles. If two marbles are selected at random, what is the probability that none is blue?

3. A bag of 10 marbles contains 3 red marbles and 7 blue marbles. If three marbles are selected at random, what is the probability that at least two marbles are blue?

4. A bag of 10 marbles contains 3 red marbles and 7 blue marbles. If three marbles are selected at random, what is the probability that two marbles are blue?

In number 4 we need to specify that probability of EXACTLY two marbles are blue. Otherwise it would be the same as 3 no?

Just wondering
Cheers
J
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Re: A bag of 10 marbles contains 3 red marbles and 7 blue [#permalink]  09 Feb 2014, 00:32
Expert's post
jlgdr wrote:
bmwhype2 wrote:
1. A bag of 10 marbles contains 3 red marbles and 7 blue marbles. If two marbles are selected at random, what is the probability that at least one marble is blue?

2. A bag of 10 marbles contains 3 red marbles and 7 blue marbles. If two marbles are selected at random, what is the probability that none is blue?

3. A bag of 10 marbles contains 3 red marbles and 7 blue marbles. If three marbles are selected at random, what is the probability that at least two marbles are blue?

4. A bag of 10 marbles contains 3 red marbles and 7 blue marbles. If three marbles are selected at random, what is the probability that two marbles are blue?

In number 4 we need to specify that probability of EXACTLY two marbles are blue. Otherwise it would be the same as 3 no?

Just wondering
Cheers
J

No. If it meant at least two, then it would be written that way.
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Re: A bag of 10 marbles contains 3 red marbles and 7 blue   [#permalink] 09 Feb 2014, 00:32
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