Question

Select the correct answer from each drop-down menu. In a bag there are two 20 bills, one 10 bill, four 5 bills, and three 1 bills. If Frank picks one bill from the bag, the expected value of the bill he chooses is ________. If one more 20 bill and one more 10 bill are added to the bag, the expected value will change to ________.

Answer 1

The expected value of the bill Frank chooses from the bag is $7.3. With the additional $20 and $10 bills, the expected value will change to approximately $9.

Step-by-step explanation:

The expected value of a bill that Frank chooses from the bag can be calculated by multiplying the value of each bill by its probability of being chosen, and then summing these up. Let's calculate:

1. There are a total of 2 + 1 + 4 + 3 = 10 bills in the bag.
2. The probability of picking a $20 bill is 2/10 = 0.2.
3. The probability of picking a $10 bill is 1/10 = 0.1.
4. The probability of picking a $5 bill is 4/10 = 0.4.
5. The probability of picking a $1 bill is 3/10 = 0.3.
6. Multiplying each value by its respective probability gives (20 * 0.2) + (10 * 0.1) + (5 * 0.4) + (1 * 0.3) = 4 + 1 + 2 + 0.3 = 7.3.

Therefore, the expected value of the bill Frank chooses from the bag is $7.3.

If one more $20 bill and one more $10 bill are added to the bag, the new probabilities become:

• The probability of picking a $20 bill becomes 3/12 = 0.25.
• The probability of picking a $10 bill becomes 2/12 ≈ 0.17.

Using the same calculations as before, the new expected value will be (20 * 0.25) + (10 * 0.17) + (5 * 0.4) + (1 * 0.3) ≈ 5 + 1.7 + 2 + 0.3 ≈ 9.

Therefore, the expected value of the bill Frank chooses will change to approximately $9 with the additional $20 and $10 bills.