Question

A carnival 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


10. What is game’s expected value of points earned for a turn?
(SHOW WORK)

Answer 1

The game’s expected value of points earned for a turn is 71.

Explanation:

Here we know that:

Points Frequency

50 55

75 32

150 13

Here points earned is a random variable.

We need to find its expected value,

Finding Expected value:

Expected value of a random variable is its mean value. So we will first find the mean value of points earned per turn from the table we are given.

Total number of turns = sum of frequencies

= 55 + 32 + 14 = 100

Total points earned = 50(55) + 75(32) + 150(13)

= 7100

Expected value of points earned for a turn = Mean value of points

= Total points/no. of turns

= 7100/100

= 71