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 ?

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AFOKE88 AFOKE88 · Answer 1 · 2021-12-17T12:56:36+01:00

The mean of w which represents the total amount won where w = x + 15 is;

w = -$4.5

We are given;

Winnings if a red chip is selected; x₁ = $5.

Now, there are 10 red chips in a bag of 20 chips.

Thus, the probability of this outcome is:

p₁ = 10/20

p₁ = 1/2

Winnings if a blue chip is selected; x₂ = $10

Now, there are 4 blue chips in a bag of 20 chips.

Thus, the probability of this outcome is:

p₂ = 4/20

p₂ = 1/5

Winnings if a yellow chip is selected; x₃ = $20

Now, there are 6 blue chips in a bag of 20 chips.

Thus, the probability of this outcome is:

p₃ = 6/20

p₃ = 3/10

Finally, the expected value is:

E(X) = 5(¹/₂) + 10(¹/₅) + 20(³/₁₀)

E(X) = $10.5

We are told that w = x - 15

where x is the amount won from selection of chip which is E(X) = $10.5

Thus;

w = 10.5 - 15

w = -$4.5

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