An urn contains 4 red, 7 blue, and 9 green balls. A set of 3 balls is randomly s
ID: 3301133 • Letter: A
Question
An urn contains 4 red, 7 blue, and 9 green balls. A set of 3 balls is randomly selected, without replacement. What is the probability that each of the balls will be: (a) of the same color (b) of all different colors Repeat the experiment under the assumption that whenever a ball is selected, its color is noted and it is then replaced in the urn before the next selection. This is known as sampling with replacement. What is the probability that each of the balls will be: (c) of the same color (d) of all different colors
Explanation / Answer
(a) Total number of ways to select 3 balls out of 20 = 20C3 = 1140
Total number of ways to select 3 balls of the same color
= 4C3 + 7C3 + 9C3
= 4 + 35 + 84 = 123
Probability that the three balls will be of same color = 123/1140 = 0.108
(b) The red ball can come in 4 ways, the blue in 7 ways and the green in 9 ways.
Total number of ways to select 3 balls with different color = 4*7*9 = 252
Probability that the three balls will have different colors = 252/1140 = 0.22
(c) Total number of ways to select three balls out of 20 with replacement = 20*20*20 = 8000
Total number of ways to select 3 balls of the same color with replacement
= 4*4*4 + 7*7*7 + 9*9*9
= 64 + 343 + 729
= 1136
Probability that the three balls will be of same color = 1136/8000 = 0.142
(d) The red ball can come in 4 ways, the blue in 7 ways and the green in 9 ways.
Total number of ways to select 3 balls with different color = 4*7*9 = 252
Probability that the three balls will have different colors = 252/8000 = 0.0315
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.