and i will buy 1,000 akorns and gift it to whoever helps me solve it. if you solve one problem i'll gift you 250, two problems i'll gift you 450, and so on.
1. Recall that a roulette wheel has 38 slots. Eighteen are red, 18 are black, and 2 are green. You can bet on 6 different numbers. If any of them comes up, you receive $6 back for each $1 bet. What is the expected loss on a $1 bet? Please round the answer to two decimal places.
a. $0.01
b. $0.08
c. $0.07
d. $0.05
e. $0.04
[SOLVED]
2. In a gambling game, you receive a payoff of $82 if you roll a sum of 4, and $7 if you roll a sum of 7 on two dice. Otherwise, you receive no payoff. What is the average payoff per play?
a. $8
b. $9
c. $6
d. $12
e. $5
[SOLVED]
3. In a carnival game, you roll 2 dice. If the sum is 5, you receive a $6 payoff. If the sum is 10, you receive a $13 payoff. What is the expected payoff?
a. $2.05
b. $1.35
c. $1.75
d. $1.55
e. $1.85
[SOLVED]
4. In a gambling game, you pick 1 card from a standard deck. If you pick an ace, you win $10. If you pick a picture card (J, Q, or K), you win $5. Otherwise, you win nothing. How much should a carnival booth charge you to play this game if they want an average profit of $0.60 per game? (hint: first find the average payout)
a. $2.12
b. $2.62
c. $2.72
d. $2.22
e. $2.52
[SOLVED]
5. You have a job working for a mathematician. She pays you each day according to what card you select from a bag. Two of the cards say $220, five of them say $100, and three of them say $50. What is your expected (average) daily pay?
$ __________ per day
[SOLVED]
6. An apartment complex has 20 air conditioners. Each summer, a certain number of them have to be replaced.
| #of AC's replaced | Probability. |
| 0 1 2 3 4 5 |
0.21 0.37 0.13 0.11 0.11 0.07 |
What is the expected number of air conditioners that will be replaced in the summer?
7. In a gambling game, you receive a payoff of $46 if you roll a sum of 10, and $7 if you roll a sum of 7 on two dice. Otherwise, you receive no payoff. What is the average payoff per play?
$ __________
