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January 29th, 2019, 04:44 PM   #1
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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!
nyuviolets is offline  
January 29th, 2019, 05:12 PM   #2
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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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