Chance calculation.

[Zealord]

I can't seem to get over this assignment, this is the question:

"Linda takes 5 marbles out of a vase filled with red and white marbles, without putting them back after taking."
Calculate the chance that she picks 2 red marbles in case the vase has 3 red and 7 white marbles.

So: She will pick 5 marbles out of the vase with 3 red marbles and 7 white marbles. What is the chance that in her pick of 5 marbles, 2 of them are red?

Thanks in advance,

[Adman]

Well I thought I would have a try at this, no idea if I got it correct but I am fairly sure I am there.

Firstly, I organised all the different combinations of possibilities that occur with only 2 of the 5 being red marbles. This I completed with a probability tree.

I got:
1. p(R,R,W,W,W)
2. p(R,W,R,W,W,)
3. p(R,W,W,R,W)
4. p(R,W,W,W,R)
5. p(W,R,R,W,W)
6. p(W,R,W,R,W)
7. p(W,R,W,W,R)
8. p(W,W,R,R,W)
9. p(W,W,R,W,R)
10. p(W,W,W,R,R,)

Now after this, I calculated the overall probabilites of each of these occurences.

For example, No. 1 would look like this:

3/10 x 2/9 x 7/8 x 6/7 x 5/6 = 1/24.

Interestingly, each of these come to a total of 1/24 and so in the end you get 10/24 which of course simplifies to 5/12.

I figure this may be the answer as it is a nice, even fraction that looks right - typical of school given questions.

My final answer is 5/12.

[Zealord]

I asked my older brother who has a major in maths. You had to use Ncr apparently.


It would be: P(2 red marbles) = (3 Ncr 2) x (7 Ncr 3) divided by 10 Ncr 5 = 0,417

5/12th is correct: 0,41666666 etc.e

You took the long road haha.

Thanks anyways

[Adman]

Ahh well glad I could help. (And get the right answer.)

Guess the long road was the only road for me.