SOLUTION: A cookie jar has 3 red marbles and 1 white marble. A shoebox has 1 red marble and 1 white marble. Three marbles are chosen at random without replacement from the cookie jar and pla
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-> SOLUTION: A cookie jar has 3 red marbles and 1 white marble. A shoebox has 1 red marble and 1 white marble. Three marbles are chosen at random without replacement from the cookie jar and pla
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Question 1181467: A cookie jar has 3 red marbles and 1 white marble. A shoebox has 1 red marble and 1 white marble. Three marbles are chosen at random without replacement from the cookie jar and placed in the shoebox. Then 2 marbles are chosen at random and without replacement from the shoebox. What is the probability that both marbles chosen from the shoebox are red? Answer by greenestamps(13200) (Show Source):
There are two ways to get 2 red marbles from the shoebox:
(1) pick all 3 red (and 0 white) from the cookie jar and put in the shoebox; then choose 2 of the 4 red from among the 5 marbles in the shoebox; or
(2) pick 2 red and the 1 white marble from the cookie jar and put in the shoebox; then choose 2 of the 3 red from among the 5 marbles in the shoebox.
The probability for the first case is
The probability for the second case is
So the probability of getting 2 red from the shoebox is 6/40+9/40 = 15/40 = 3/8.
