Answer to Question #323811 in Statistics and Probability for Bless

Question #323811

An urn contains ten marbles, of which five are green, two are blue, and three are red. Three marbles are to be drawn from the urn, one at a time without replacement. What is the probability that all three marbles drawn will be green?

1
Expert's answer
2022-04-11T12:48:01-0400

 The probability of choosing a green marbles on the first draw is

P1=510=12.P_1=\cfrac{5}{10}=\cfrac{1}{2}.

Since we do not put it back, there are 9 marbles, 4 of which are green. The second green has probability

P2=49.P_2=\cfrac{4}{9}.

Now there are 8 marbles, 3 of which are green,

P3=38.P_3=\cfrac{3}{8}.

So, the probability that all three marbles drawn are green

P=P1P2P3=124938=112.P=P_1\cdot P_2\cdot P_3=\cfrac{1}{2} \cdot\cfrac{4}{9} \cdot\cfrac{3}{8} =\cfrac{1}{12}.


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