Thread: Probability with different possibilities

I completely forget how to do this, any help would be greatly appreciated.

Alex has a bag containing 5 yellow, 6 blue, and 7 purple marbles. Find the probability of him choosing, without replacement, 2 purples and a blue in any order in 4 picks.

(^If it were 3 picks, I'd have no problem, but I forget how to do this type of problem...)

Originally Posted by Sconts

I completely forget how to do this, any help would be greatly appreciated.

Alex has a bag containing 5 yellow, 6 blue, and 7 purple marbles. Find the probability of him choosing, without replacement, 2 purples and a blue in any order in 4 picks.

I do not understand what you mean by "picking 4".

Originally Posted by ThePerfectHacker

I do not understand what you mean by "picking 4".

Sorry, let me clarify:
He picks 4 marbles. 2 must be purple, 1 must be blue, and I think the last one can be anything...

would it be like, 18P4 * (7/18)*(6/17)*(6/16)*(15/15) ?
or something?
blah sorry, completely blanking on this section.

Originally Posted by Sconts

Sorry, let me clarify:
He picks 4 marbles. 2 must be purple, 1 must be blue, and I think the last one can be anything...

I recommend to divide the problem into cases.

Case 1: 2 purble, 1 blue, 1 yellow.

Case 2: 2 purble, 1 blue , 1 blue = 2 purble , 2 blue.

Case 3: 2 purble, 1 blue, 1 purble = 3 purble , 1 blue.

Now, you find the probability for each one, which is much easier. And them you add them up.