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?
E1 = all three marbles are red, leaving one white marble
E2 = two marbles are red and one marble is white, leaving one red marble
All of them have same probability of leaving behind
P(E1) = 1/4
P(E2) = 3/4
Let W be the event of choosing two red marbles from the shoebox
P(W) = P(W/E1) * P(E1) + P(W/E2) * P(E2)
= 4C2/5C2 * 1/4 + 3C2/5C2 * 3/4
= 15/40
= 3/8
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