A box contains 5 red marbles, 4 blue marbles and 6 green marbles.

Question

a. Find the probability that two marbles are drawn, without replacement, and both are red.

b. Find the probability that two marbles are drawn, with replacement, and both are green.

c. Find the probability that two marbles are drawn, without replacement, and one is blue and one is red.

Answer 1

15 marbles total

a. C(5,2) ways to draw two red marbles out of 5.. C(15,2) ways to draw 2 marbles out of 15. probability to draw 2 red marbles in a row without replacement is C(5,2)/C(15,2) = 2/21.

b. Since sampling with replacement, 6/15 = 2/5 chance on both 1st and 2nd draws to pick green marble. Chance of drawing green on both draws is 2/5 * 2/5 = 4/25

c. C(5,1) ways to draw one red marble out of 5. C(4,1) ways to draw 1 blue marble out of 4. C(5,1)*C(4,1) ways to draw one red and one blue marble. C(15,2) ways to draw 2 marbles out of 15. probability to draw one red and one blue marble without replacement is C(5,1)*C(4,1)/C(15,2) = 4/21.