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January 29th, 2019, 05:44 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!
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January 29th, 2019, 06:12 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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