Question

You have a bag containing 15 marbles, 5 red, 5 blue, 5 green.

a.) You draw 3 marbles one at a time and return each of them back to the bag before drawing the next one. What is the probability that you pick differently colored marbles?

b.) You draw 3 marbles one at a time without returning them. What is the probability that you pick differently colored marbles?

c.) You draw 3 marbles one at a time without returning them. What is the probability you pick marbles of the same color?

Answer 1

a) P(different colored marbles, with replacement) = P(selecting any marble first) x P(selecting marble of the color that is not of the first color) x P(selecting marble of color that was not selected n first 2 trials)

= 15/15 x 10/15 x 5/15

= 0.2222

b) P(different colored marbles, without replacement) = P(selecting any marble first) x P(selecting marble of the color that is not of the first color) x P(selecting marble of color that was not selected n first 2 trials)

= 15/15 x 10/14 x 5/13

= 0.2747

c) P(you pick marbles of the same color) = P(3 red) or P(3 blue) or P(3 green)

= 3 x (5/15 x 4/14 x 3/13)

= 0.0659