Grr, a little help with a probability question please?

Question

40 blue, 40 red, 20 green. 60 of these are large. What's the probability of choosing 3 large, blue, without replacement?

I can do this if there aren't large and small. If they are all the same size, the answer is 6.1% chance for 3 blue.

How do you factor in the 60 large?

Thanks!

Answer 1

Color and size are not related (there is no relationship given, between color and size). Thus they are statistically independent events. It follows that:

P(3BLUE AND 3LARGE) = P(3BLUE) × P(3LARGE)

So we want:

P(3BLUE) = 40C3 / 100C3
P(3LARGE) = 60C3 / 100C3

P(3BLUE AND 3LARGE)

= 40C3 × 60C3 / (100C3)²

P(3BLUE) approx= 6.11 %
P(3LARGE) approx= 21.16 %

P(3BLUE AND 3LARGE) approx= 1.29305474 %

If you don't know what 100C3 means, it is a binomial coefficient, read "100 choose 3." It is the number of ways to choose 3 things out of 100. See:
http://en.wikipedia.org/wiki/Binomial_coefficient