Question

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 1

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