Question

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 answer a: $10. 50 a $4. 50 answer b: $4. 50 b −$4. 50 answer c: negative 4. 50 dollars c −$6. 50 answer d: negative 6. 50 dollars d −$10. 50.

Answer 1

The mean of the random variable w that represents the total amount won is; -$4.50

We are given quantity of chips inside the bag as;

• Number of red chips = 10

• Number of blue chips = 4

• Number of Yellow chips = 6

Total number of chips = 20

Thus;

• P(Red chips) = 10/20 = 0.5

• P(blue chips) 4/20 = 0.2

• P(Yellow Chips) = 6/20 = 0.3

Amount won from the selection of Red Chip = 0.5 * $5 = $2.5

Amount won from the selection blue Chip = 0.2 * $10 = $2

Amount won from selection of yellow chip = 0.3 * $20 = $6

Thus;

x = $2.5 + $2 + $6

x = $10.5

We are told that total amount won is gotten from;

w = x − 15

Thus;

w = 10.5 - 15

w = -$4.50

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