## 20 marbles: 8 red, 7 white, 5 blue; draw 4 w/o replacement

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
lawrence
Posts: 15
Joined: Wed Apr 01, 2009 10:48 pm

### 20 marbles: 8 red, 7 white, 5 blue; draw 4 w/o replacement

I have twenty marbles in a bowl: eight are red, seven are white, and five are blue. Let's suppose I draw four marbles without replacement.

A. What is the probability that none of the four is red?
B. What is the probability that I draw at least one of each color?

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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I was really hoping somebody better qualified would jump in on this one....

A) You're choosing four of the twenty. There are C(20,4) ways to choose four of twenty.

You want to make sure that, of the eight red, you pick zero. There are C(8,0) ways to do this.

You want to make sure that, of the other twelve you pick some random four. There are C(12,4) ways to do this.

Then the probability of picking four, none of which is red, should (I believe) be:

. . . . .$\frac{C(12,4)\, C(8,0)}{C(20,4)}$