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A player pays $15 to play a game in which a chip is randomly selected from a bag of chips. The bag contains 10 red chips, 4 blue chips, and 6 yellow chips. The player wins $5 if a red chip is
selected, $10 if a blue chip is selected, and $20 if a yellow chip is selected. Let the random variable X represent the amount won from the selection of the chip, and let the random variable W
represent the total amount won, where W= X - 15. What is the mean of W?
$10.50
B
$4.50
-$4.50
D
- $6.50
E
-$10.50

Respuesta :

Answer:

C. -$4.50

Step-by-step explanation:

To find the mean of W we must first find the mean of X. So, 10/20*5+4/20*10+6/20*20=10.5

Then because mean is impacted by transformations, the mean of W=the mean of X-15=10.5-15=-$4.50

facundo3141592

Here we need to find the expected value of the given probabilistic game.

The correct option is B: -$4.50

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For an event with outcomes {x₁, x₂, ...}, each one with probability {p₁, p₂, ...}, the expected value is defined as:

[tex]EV = x_1*p_1 + x_2*p_2 + ...[/tex]

Here the outcomes are:

x₁ = winning $5.

This happens if a red chip is selected, and there are 10 red chips in a bag of 20 chips, so the probability is:

p₁ = 10/20 = 1/2

x₂ = winning $10

This happens if a blue chip is selected, and there are 4 blue chips out of 20 chips, so the probability is:

p₂ = 4/20 = 1/5

x₃ = winning $20

This happens if a yellow chip is selected, and there are 6 of these in a total of 20, then the probability is:

p₃ = 6/20 = 3/10

Now we can compute the expected value:

[tex]EV = \$ 5*(1/2) + \$ 10*(1/5) + \$ 20*(3/10) = \$ 10.50[/tex]

Now if you also take in mind that you need to pay $15.00 to play, we will see that the mean of W, the amount that you won, is:

W = $10.50 - $15.00 = -$4.50

Which means that in average, you lose $4.50

If you want to learn more, you can read:

https://brainly.com/question/18523098

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