A six- sided die is weighted so that rolling a two, four, or six is equally likely. In addition, rolling a one is twice as likely as rolling a two, rolling a three is 3 times as likely as rolling a one, and rolling and one and five are equally likely. What is the probability that an even number is rolled

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A six- sided die is weighted so that rolling a two, four, or six is equally likely. In addition, rolling a one is twice as likely as rolling a two, rolling a three is 3 times as likely as rolling a one, and rolling and one and five are equally likely. What is the probability that an even number is rolled? Give your answer as a fraction.
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Step 1

Let x be the probability of getting two. Therefore we have

x P(x)
1 2x
2 x
3 3(2x) =6x
4 x
5 2x
6 x
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