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An urn contains 5 red, 6 blue, and 8 green balls. If a set
Chapter 2, Problem 28P(choose chapter or problem)
Problem 28P
An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what is the probability that each of the balls will be (a) of the same color? (b) of different colors? Repeat 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.
Questions & Answers
QUESTION:
Problem 28P
An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what is the probability that each of the balls will be (a) of the same color? (b) of different colors? Repeat 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.
ANSWER:
Solution :
Step 1 of 2:
Given an urn contains 5 red, 6 blue, and 8 green balls.
Then, if a set of 3 balls is randomly selected.
We know that the total number of balls is 19.
Our goal is:
a). We need to find the probability that each of the balls will be the same color.
b). We need to find the probability that each of the balls will be the different colors.
a). Let the number of possible ways for selecting 3 balls of 19 balls is
ways.
Let the number of possible ways of selecting 3 blue balls out of 6 balls is
ways.
Let the number of possible ways of selecting 3 green balls out of 8 red balls is
ways and
Let the number of possible ways of selecting 3 red balls out of 5 red balls is
ways.
Then the probability is given by
=
=
=
=
= 0.0887
Therefore, the probability that each of the balls will be same color is 0.0887.