Answer to Question #323811 in Statistics and Probability for Bless

Question

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?

Answer 1

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

$P_1=\cfrac{5}{10}=\cfrac{1}{2}.$

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

$P_2=\cfrac{4}{9}.$

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

$P_3=\cfrac{3}{8}.$

So, the probability that all three marbles drawn are green

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