Question

It costs $5 to play the following game. You roll a dice and you spin the spinner that is seen in the image. If the sum of your roll and your spin is 6 or 8, you win $5. If your sum is 11 you win $20. If you get any other sum then you lose.

1. List the elements in the sample set.

2. Find the expected value for this game.

3. Is the game in your favor?

Answer 1

What's the image? We kind of need to see the spinner to figure out the problem. Or could you describe it?

Answer 2

The spinner has 3 sections 2,7, and 5

Answer 3

Okay then. Give me a moment.

Answer 4

Thank you

Answer 5

And I'm assuming it's a six sided die?

Answer 6

yes

Answer 7

Okay. So for the first one, we can get a couple of different sums. Since we can get all the numbers 1-6 plus either 2, 7, or 5, we have the following list:

{3,4,5,6,7,8,9,10,11,12,13}

So that's the answer to the first question. For the next one, the expected value is just the sum of all the possible numbers times the probability of a single one happening. So it's\[(3+4+5+6+7+8+9+10+11+12+13) / 11\]Which is just 8. So the expected value is 8.

Answer 8

For the last one, I'm just going to give you some pointers, since you should be able to figure it out. A couple things are really important - first, we need to figure out repetition of certain numbers. Secondly, we need to take into account the way the problem changes if you earn different amounts of money for different spins. Call me over if you have any additional questions.

Answer 9

Thanks for the medal, by the way.

Answer 10

Okay thank you that helps a lot!

Answer 11

No problem. Good luck!