probability

70R573N:

Suppose U is a population consisting of 200 marbles in which 25 of them are red. What is the probability of getting 3 red marbles in a sample of 7?

If you had a great many more marbles and 25/200 = 1/8 were red then this would be a much mor standard problem. Because each time a marble is chosen i could say that the chance of getting a red one is 1/8. the events would be independent of one another.

If that were the case then the probability of getting 3 reds would be 7C3 * (1/8) ³ * (7/8) ⁴ = 35 * (1/8) ³ * (7/8) ⁴ = 0.04007101 = about 4%


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[size=150]Let me think about the real question.[/size]

How many ways can 3 red and 4 others be chosen 25C3 * 175C4
How many combinations of 7 are there altogether 200C7

Probability = 25C3 * 175C4 / 200C7 ==> 0.038019 ==> about 3.8%

I think that maybe 3.8% is the right answer but I am not very good at probability so I want another mathematician to look at it.

SOMEONE ELSE - PLEASE TAKE A PROPER LOOK - I WANT TO KNOW HOW TO DO THIS TOO - Melody

I'm pretty sure Melody is correct!!

To see this further, here's what I used to tell my students when I was tutoring::

Assume - if we could do so - that we are going to take ALL the sets that we can make by choosing ANY 7 marbles out of the 200, and we're going to lay all these sets on the ground.
The number of these sets = C(200, 7).

Now, I'm going to walk around and pick up certain sets. But the only ones I'm interested in are the ones that contain 3 red marbles and 4 blue ones. Now, in each set I have seven "slots."
The first 3 slots will contain red marbles and the last 4 will contain blue ones. Note that the order of marbles really doesn't matter - one ordering is as good as any other.

Well, the number of total sets I can make consists of two subsets of things in each set of seven marbles - namely, choosing any 3 red marbles from 25 and choosing any 4 marbles from 175.. So, the total number of ways to do this is just [ C(25,3) * C (175, 4)].

So, the total probability = [The number of sets of things we're interested in picking up] / [The total number that were laying on the ground before we picked any of them up]

And, as Melody's numbers attest, this is just [ C(25,3) * C (175, 4)] / [C(200,7)] = 3.8%

I agree.

Thank you ILS