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22 January, 06:07

A fair, 12-sided die has numbers on each of its faces. There are three faces with a 1, three faces with a 2, one face with a 3, four faces with a 4, and one face with a 5.

What is the expected value when rolling this die?

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  1. 22 January, 06:12
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    2.75

    Step-by-step explanation:

    Let's start by making a frequency table. If there is one face, you have a 1/12 chance of getting the value--that's what the "frequency" column means.

    Face Frequency

    1 3/12

    2 3/12

    3 1/12

    4 4/12

    5 1/12

    Now to get E (X) we need to multiply each face by the frequency of it occuring and add all these together:

    E (X) = 1 (3/12) + 2 (3/12) + 3 (1/12) + 4 (4/12) + 5 (1/12)

    = 2.75
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