Question

When Josiah buys a ticket at the local movie theater, he receives 100 reward points to use toward future purchases. He is offered a scratch-off card instead of the points, which will allow him to try for a higher point value. The three possible point awards on the scratch-off card are 25, 100, and 120. There is an equal number of cards for each point award in the stack he chooses the card from.

Which statement is true?


A
The best option is to take the 100 points because the expected value of the points from the scratch-off card is less than 100 points.

B
The best option is to take the scratch-off card because two of the three possible point values on the card are the same or greater than the 100 points.

C
The best option is to take the scratch-off card because the 120-point value that is on the card is greater than 100 points.

D
The best option is to take the 100 points because the probability of being awarded more than 100 points on the scratch-off card is zero.

Answer 1

The best option is to take the 100 points because the expected value of the points from the scratch-off card is less than 100 points option (A) is correct.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

Since, there is an equal number of cards of point 25, 100, and 120

P(x =25) = P(x =100) = P(x =200)  = 1/3

x:     25     100   120

P(x):   1/3    1/3     1/3

The expected value is:

E(x) = 25×(1/3) + 100×(1/3) + 125×(1/3)

E(x) = 245/3 < 300/3  = 100

Thus, the best option is to take the 100 points because the expected value of the points from the scratch-off card is less than 100 points option (A) is correct.

Learn more about the probability here:

brainly.com/question/11234923

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