Balls in Urns

Practice Problems
1. An urn contains 4 red balls and 5 green balls. For each of the following
problems, the balls are picked and not replaced.
(a) If one ball is picked at random, what is the probability it is red?
(b) If two balls are picked at random, what is the probability they are both
red?
(c) If two balls are picked at random, what is the probability they are the same
color?
(d) If two balls are picked at random, what is the probability they are different
colors?
(e) If three balls are picked at random, what is the probability they are all
green?
2. An urn contains 4 red balls and 5 green balls. For each of the following
problems, the balls are picked and are replaced.
(a) If two balls are picked at random, what is the probability they are both
red?
(b) If two balls are picked at random, what is the probability they are the same
color?
(c) If two balls are picked at random, what is the probability they are different
colors?
(d) If ten balls are picked at random, what is the probability they are all green?
3. An urn contains 2 red balls, 6 blue balls, and 3 green balls. For each of
the following problems, the balls are picked and not replaced.
(a) If one ball is picked at random, what is the probability it is red?
(b) If two balls are picked at random, what is the probability they are both
blue?
(c) If three balls are picked at random, what is the probability they are the
same color?
(d) If two balls are picked at random, what is the probability they are different
colors?
(e) If four balls are picked at random, what is the probability they are all blue?
4. An urn contains 2 red balls, 6 blue balls, and 3 green balls. For each of
the following problems, the balls are picked and are replaced.
(a) If two balls are picked at random, what is the probability they are both
blue?
(b) If two balls are picked at random, what is the probability that one is green
and one is blue?
(c) If three balls are picked at random, what is the probability they are the
same color?
(d) If four balls are picked at random, what is the probability they are all blue?

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