Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

math help pls! no idea what to do?

A fair die has 8 faces. Seven of the faces are numbered with the first seven prime numbers and the eight side is labelled with a mystery number. If the expected value of the die is 11, what is the mystery number? Show your work and include a probability distribution table.

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  • 1 month ago

    The first 7 prime numbers are:

    2, 3, 5, 7, 11, 13, 17

    Add those up:

    2 + 3 + 5 + 7 + 11 + 13 + 17 = 58

    In order for the expected value to average out to 11 (for 8 sides), the total of all the numbers must be 88.

    So the mystery number is 30.

    Double-check:(2 + 3 + 5 + 7 + 11 + 13 + 17 + 30) / 8

    = 88 / 8

    = 11

    You can create a probability distribution table, but since it is a fair die, they each have a probability of 1/8.

    x | P(x)

    ----------

    2 | 1/8

    3 | 1/8

    5 | 1/8

    7 | 1/8

    11 | 1/8

    13 | 1/8

    17 | 1/8

    30 | 1/8

    And the expected value is:

    E(X) = 2 * 1/8 + 3 * 1/8 + ... + 17 * 1/8 + 30 * 1/8

    E(X) = (2 + 3 + 5 + ... + 17 + 30) / 8

    E(X) = 88 / 8

    E(X) = 11

    Answer:

    30

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  • Numbers: 2, 3, 5, 7, 11, 13, 17, x

    Each has an equal probability of 1/8 = 12.5%

    The probability distribution table will appear flat (uniformly distributed)

    E(x) = 11 = (1/8)(2) + (1/8)(3) + (1/8)(5) + (1/8)(7) + (1/8)(11) + (1/8)(13) + (1/8)(17) + (1/8)(x)

    88 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + x

    88 - 58 = x

    x = 30

    Therefore, the unknown value is 30

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