Question

35/163
3. A bag contains 6 red, 8 yellow and 4
green balls. 3 balls are drawn randomly.
What is the probability that the balls drawn
contain balls of different colours ? *
(2 Points)
9/17​

Answer 1

Answer:

The big ambiguity in this question is around the phrase “different colours” — does that mean that no two are alike, or the not all three are the same? After all, a selection with two reds and one yellow contains two different colors (or colours).

Let’s take the not-all-the-same question first.

P(all green) = 4C3 / 18C3 = 4 / 816

P(all yellow) = 8C3 / 18C3 = 56 / 816

P(all red) = 6C3 / 18C3 = 20 / 816

P(all same) = P(all red) + P(all yellow) + P(all green) = (4 + 56 + 20) / 816 = 9.8%

P(not all same) = 1 - P(all same) = 100% - 9.8% = 90.2%

Easy peasy. How about the all-different question?

With three balls drawn, this is just one of each color.

C(a green) * C(a red) * C(a yellow) / C(any three) = 4C1 * 6C1 * 8C1 / 18C3 = 192/816 = 23.5%

So the answer could be 23.5% or 91.2% depending on what the question means. As with most problems of this ilk, resolving the ambiguity in the question and mapping it onto what real world situation you are trying to solve is the important part. There aren’t many scenarios where swapping either of those answers for the other is going to be okay.

this was from quora

Answer 2

Answer:

The big ambiguity in this question is around the phrase “different colours” — does that mean that no two are alike, or the not all three are the same? After all, a selection with two reds and one yellow contains two different colors (or colours).

Let’s take the not-all-the-same question first.

P(all green) = 4C3 / 18C3 = 4 / 816

P(all yellow) = 8C3 / 18C3 = 56 / 816

P(all red) = 6C3 / 18C3 = 20 / 816

P(all same) = P(all red) + P(all yellow) + P(all green) = (4 + 56 + 20) / 816 = 9.8%

P(not all same) = 1 - P(all same) = 100% - 9.8% = 90.2%

Easy peasy. How about the all-different question?

With three balls drawn, this is just one of each color.

C(a green) * C(a red) * C(a yellow) / C(any three) = 4C1 * 6C1 * 8C1 / 18C3 = 192/816 = 23.5%

So the answer could be 23.5% or 91.2% depending on what the question means. As with most problems of this ilk, resolving the ambiguity in the question and mapping it onto what real world situation you are trying to solve is the important part. There aren’t many scenarios where swapping either of those answers for the other is going to be okay.