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January 29th, 2019, 05:44 PM  #1 
Newbie Joined: Jul 2015 From: N/A Posts: 16 Thanks: 0  Another probability question!
An urn contains 3 blue marbles and 2 red marbles. If you randomly choose 3 marbles without replacement, what is the probability that: (a) Exactly one marble is red? (b) All three marbles are blue? (c) At least one marble is blue? (d) At most one marble is blue? Thank you in advance! 
January 29th, 2019, 06:12 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,299 Thanks: 1222 
in general If you have $r$ red marbles and $b$ blue marbles and you choose $k = n_r + n_b$ marbles $P[\text{you pick }n_r \text{ red marbles, and }n_b \text{ blue marbles}]= \dfrac{\dbinom{r}{n_r}\dbinom{b}{n_b}}{\dbinom{r+b }{n_r+n_b}}$ That should get you started 

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