Question

Homework: Section 3.3 Score: 5.5/8 5/8 answered • Question 6 An urn contains 9 red marbles, 5 white marbles, and 8 blue marbles marbles. A child randomly selects three (without replacement) from the urn. Round to four decimal places. a. Find the probability all three marbles are the same color. b. Find the probability that none of the three marbles are white. Submit Question esc 30

Answer 1

Probability = Favorable outcomes / Total Outcomes

Total marbles = 9R + 5W + 8B = 22

When we have without replacement, the denominator keep reducing by 1 on every pick. If the same color is being picked,then the numerator also reduces by 1..

(a) Probability that they are all the same color = P(All Red) + P(All white or P(All Blue)

P(All Red) = 9/22 * 8/21 * 7/20 = 504 / 9240

P(All White) = 5/22 * 4/21 * 3/20 = 60 / 9240

P(All Blue) = 8/22 * 7/22 * 6/22 = 336/9240

Therefore the required probability = 504 / 9240 + 60 / 9240 + 336 / 9240 = 900/9240 = 0.0974

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(b) The number of non white marbles are 22 - 5 = 17

Therefore The probability of choosing a non white marble without replacement

Case 1: All are Blue: The probability is = 8/22 * 7/22 * 6/22 = 336/9240

Case 2: All Red. The probability = 9/22 * 8/21 * 7/20 = 504/9240

Case 3: 2 Red and 1 Blue = 9/22 * 8/21 * 8/20 * (3!/2!) = 1728/9240

We multiply by 3! as there are 6 ways in which we can pick, but we divide by 2! to factor the same colored balls.Therefore there are 3 orders in which the ball can be picked RRB, RBR and BRR..

Case 4: 1 Red and 2 Blue = 9/22 * 8/21 * 7/20 * (3!/2!) = 1512/9240

Therefore the required probability = 336/9240 + 504/9240 + 1728/9240 + 1512/9240 = 4080/9240 = 0.4416