Question

A bag contains 1 white chip, 2 blue chips, and 3 red chips. What is the probability of randomly selecting of two chips (without replacement) that are different colors?

Answer 1

You should try drawing a probability tree.
Either that, or you can use the multivariate hypergeometric distribution.

Answer 2

So, \(\dfrac{11}{15}\)?

Answer 3

I think I got it, but I'm confused how it works...

Answer 4

There are three mutually exclusive events:
1) Select white first and a different color next:
\[P(w)=\frac{1}{6}\times 1=\frac{1}{6}\]
2) Select a blue first and a different color next:
\[P(b)=\frac{2}{6}\times \frac{4}{5}=\frac{8}{30}\]
3) Select a red first and a different color next:
\[P(r)=\frac{3}{6}\times \frac{3}{5}=\frac{9}{30}\]
Therefore the required probability is:
\[P=\frac{1}{6}+\frac{8}{30}+\frac{9}{30}=you\ can\ calculate\]