What is the expectation of X?

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.2: Probability
Problem 31E
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Question

An urn holds 4 red, 3 blue, and 2 green marbles.
Three marbles are selected, altogether, without replacement.
Let X be the number of different colors obtained.
(For example, if you get 3 blues, then X = 1, but if you get 2 reds and a green, then X = 2.)

What is the expectation of X?

Give an answer in decimal format and correct to at least 4 decimal place accuracy.

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