My Question (Reposted)
A bag contains 4 blue balls and 5 yellow balls. You take three balls out without returning them to the bag. In how many ways can you pick out three balls of the same color? In addition to posting your answer, David asks that you also indicate the level of difficulty you think the question falls under (A, B, or C level).
danielsanford2C: Feb. 2, 2015, 2:53 a.m.
To start this I would break the question up into two parts: one if you pick three blue balls and one if you pick three yellow balls. First, looking at the blue balls you have a 4/9 chance to pick a blue ball for the first ball, 3/8 for the second and 2/7 for the third so you have (4/9 * 3/8 * 2/7) for our purposes this is 4 X 3 X 2. Next, looking at the yellow balls, you have a 5/9 chance for the first, 4/8 for the second and 3/7 for the third yielding (5/9 * 1/2 * 3/7) we use 5 X 4 X 3. After this I am unsure, but I think you add the two numbers to give the total number of possibilities. So the answer would be ((5X4X3) + (4X3X2)). If I solved this correctly I think it is a B level question.
AZobi: Feb. 2, 2015, 12:38 p.m.
Unfortunately, your answer does not match mine. I do, however, appreciate your attempt. :) On a side note, does anyone know how long I should wait until I post my answer?
weisbart: Feb. 3, 2015, 2:47 p.m.
The challenge is on!!!
AZobi: Feb. 4, 2015, 7:56 p.m.
Joyce2E correctly stated 14 on the other page. Should I show the work that explains why her answer is correct? I believe that this question is a B level question. It's not as difficult as the A level questions we have been exposed to, but it isn't as simple as the level C questions either. This question is fairly similar to questions from Lesson 6 in the book. To danielsanford2C: You were not entirely incorrect. Your approach would have been perfect if I had asked for the probability. ( (4/9 * 3/8 * 2/7) +(5/9 * 1/2 * 3/7) = 0.1666666667) On the other hand, getting rid of the denominators was not correct.
iraianne: Feb. 7, 2015, 11:25 p.m.
So its 14 because for the case of the blue balls you have (4 choose 3) and for the yellow balls you have (3 choose 3). Solving it out would give you 14. Yah I agree it seems like a level B question.
weisbart: Feb. 8, 2015, 11:24 a.m.
I agree, I think it is a solid B level question. Good job to everyone! The reason is that it requires the usage of cases. This always makes things more complicated.
Soniakumr: Feb. 8, 2015, 3:11 p.m.
Does anyone want to try finding the probability of this?