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

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

30

• 1 month ago

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