Question

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Computing expected value in a game of chance
QUESTION
Scott is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a numbered slice at random.
This game is this: Scott spins the spinner once. He wins $1 if the spinner stops on the number 1, $3 if the spinner stops on the number 2, $5 if the spinner
stops on the number 3, and $7 if the spinner stops on the number 4. He loses $1.25 if the spinner stops on 5 or 6.
(a) Find the expected value of playing the game.
dollars
(b) What can Scott expect in the long run, after playing the game many times?
Scott can expect to gain money.
He can expect to win dollars per spin.
Start
Scott can expect to lose money.
He can expect to lose dollars per spin.
Scott can expect to break even (neither gain nor lose money).
00 EXPLANATION
0 0/5

Answer 1

Answer:$0.25

Explanation:

To find the expected value of playing the game, we need to multiply the payoff for each possible outcome by its probability and then add up all the values.

Let's first find the probabilities of each outcome:

- Probability of spinning1:1/6

- Probability of spinning2:1/6

- Probability of spinning3:1/6

- Probability of spinning4:1/6

- Probability of spinning5 or6:2/6( or1/3)

Now let's calculate the expected value:

Expected value=(1/6*$1)+(1/6*$3)+(1/6*$5)+(1/6*$7)+(1/3*-$1.25)

Expected value=$0.25

So the expected value of playing the game is$0.25 per spin.

In the long run, Scott can expect to gain money since the expected value is positive. However, this doesn't guarantee that he will actually win money every time he plays the game, as there is still a certain degree of randomness involved in each spin.