Question

1. Suppose we have a bag with $10$ slips of paper in it. Eight slips have a $3$ on them and the other two have a $9$ on them.

What is the expected value of the number shown when we draw a single slip of paper?

2. Suppose we have a bag with $10$ slips of paper in it. Eight slips have a $3$ on them and the other two have a $9$ on them.

What is the expected value of the number shown if we add one additional $9$ to the bag?

3. Suppose we have a bag with $10$ slips of paper in it. Eight slips have a $3$ on them and the other two have a $9$ on them.

What is the expected value of the number shown if we add two additional $9$'s (instead of just one) to the bag?

4. Suppose we have a bag with $10$ slips of paper in it. Eight slips have a $3$ on them and the other two have a $9$ on them.

How many $9$'s do we have to add to make the expected value equal to $6$?

Thanks!

Answer 1

It would help if you proofread your questions before you posted them.

First of all, the dollar sign only goes BEFORE the value, e.g., $10.

Second, if it is not a dollar amount, do not use a dollar sign ($).

Answer 2

the reason for the dollar signs is because they copy pasted from AoPS which uses Latex. STOP CHEATING ON YOUR HOMEWORK!!!

Answer 3

For number 2:
Question: Suppose we have a bag with $10$ slips of paper in it. Eight slips have a $3$ on them and the other two have a $9$ on them. What is the expected value of the number shown if we add one additional $9$ to the bag?
Answer: 3(8/11) + 9 (3/11) = 24/11 + 27 /11 = 51/11 ≈ 4.63

Answer 4

For number 3:
Question: Suppose we have a bag with 10 slips of paper in it. Eight slips have a 3 on them and the other two have a 9 on them. What is the expected value of the number shown if we add two additional 9's (instead of just one) to the bag?
Answer: 3 ( 8/12) + 9(4/12) = 24/12 + 36/12 = 60/12 = 5

Answer 5

For number 1:
Question: Suppose we have a bag with $10$ slips of paper in it. Eight slips have a $3$ on them and the other two have a $9$ on them. What is the expected value of the number shown when we draw a single slip of paper?
Answer: 3(8/10) + 9(2/10) = 24/10 + 18/10 = 42/10 = 21/5 = 4.2

Answer 6

For number 4:
Question: Suppose we have a bag with 10 slips of paper in it. Eight slips have a 3 on them and the other two have a 9 on them. How many 9's do we have to add to make the expected value equal to 6?
Answer: The expected value being 6 would imply that the amounts of 3 and 9 must be equal to make the probabilities be equal, which is done by adding 6 9’s. So the answer is 6.