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Harlene tosses two number cubes. If a sum of 8 or 12 comes up, she gets 9 points. If not, she loses 2 points. What is the expected value of the number of points for one roll? Negative two-thirds Negative one-sixth one-sixth Two-thirds.

Sagot :

Facundo3141592idn

We want to get the expected value for the given experiment, we will see that it is equal to -1/6 points, so the correct option is "negative one-sixth"

For an experiment with events {x₁, x₂, ..., xₙ}, each one with probability {p₁, p₂, ..., pₙ}, the expected value is given by:

EV = x₁*p₁ + ... + xₙ*pₙ

Here we have two events:

  • x₁ = she gets 9 points.
  • x₂ = she loses 2 points.

Let's find the probabilities of each one of these.

She gets 9 points if the sum of the two dice is equal to 8 or 12.

Each dice has 6 outcomes.

Then a combination of two dice has a total of 6*6 = 36 outcomes.

The outcomes that add to 8 or 12 are:

dice 1   dice 2  sum

2           6            8

3           5            8

4           4            8

5          6             8

6           2            8

6           6            12

So 6 out of the 36 outcomes, then the probability of this event is:

p₁ = 6/36 = 1/6

And the other event is for all the other outcomes, so the probability is just:

p₂ = 5/6

Then the expected value is:

EV = (+ 9 points)*(1/6) + (-2 points)*(5/6)  = -1/6 points.

So the correct option is negative one-sixth.

If you want to learn more about expected value, you can read:

https://brainly.com/question/22097128

Wow2noobidn

Answer:

-1/6

Step-by-step explanation:

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