Acarnival game has the possibility of scoring 50 points, 75 points, or 150 points per turn. the probability of scoring 50 points is 60%, 75 points is 30%, and 150 points is 10%. the game operator designed a simulation using a random number generator to predict how many points would be earned for a turn.
integer value, points, frequency
0.5 50 55
6.8 75 32
9 150 13
what is game’s expected value of points earned for a turn?

The game's expected value of points for a turn is 71

Step-by-step explanation:

* Lets explain how to solve the problem

- Expected value is the average value of a random variable over a

  large number of experiments

- The expected value measures the center of the probability

  distribution

- The expected value is the mean of the random variable

* Lets solve the problem

- The game operator designed a simulation using a random number

  generator to predict the points would be earned for a turn

∵ The frequency of scoring 50 points is 55

∵ The frequency of scoring 75 points is 32

∵ The frequency of scoring 150 points is 13

∵ The expected value = mean value

∵ Mean value = sum of the total points ÷ total frequency

∵ The sum of the total points = 50(55) + 75(32) + 150(13)

∴ The sum of the total points = 2750 + 2400 + 1950

∴ The sum of the total points = 7100

∵ The total frequency = 55 + 32 + 13

∴ The total frequency = 100

∴ The mean = 7100 ÷ 100 = 71

∵ The total frequency = the total turns

∵ The mean value = the expected value

∴ The expected value = 71 for a turn

* The game's expected value of points for a turn is 71

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