Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 4 or a 2, nothing otherwise. What is the expected amount to win (or lose)
For a fair die roll, we have here:
P(2 or 4) = 2/6 = 1/3
Therefore, the expected payoff here is computed as:
E(Payoff) = 5*(1/3) = 5/3
Therefore the expected total profit / loss is computed here
as:
= - Cost of fair die + E(Payoff)
= -2 + (5/3)
= -1/3
Therefore -1/3 is the required expected profit here while (5/3) is the expected payoff here.
Suppose you pay $2.00 to roll a fair die with the understanding that you will get...
Suppose you pay $0.30 to roll a fair 9-sided die with the understanding that you will get $0.70 back for rolling a 1, 2, or 3. Otherwise, you get no money back. What is your expected value of gain or loss?
Suppose you pay $1.30 to roll a fair 15-sided die with the understanding that you will get $3.10 back for rolling a 1, 2, 3, or 4. Otherwise, you get no money back. What is your expected value of gain or loss? Round your answer to the nearest cent (i.e. 2 places after the decimal point), if necessary. Do NOT type a "$" in the answer box. Expected value of gain or loss: $
please answer clearly 5. Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 4 or a 2, nothing otherwise. What is the expected amount you win (or lose)? A) $-1.00 B) S-0.33 C) S-2.33 D) S-1.33 E) None of the Above 15. Use the given sample data: construct a 95% confidence interval for the population mean: n = 13, xbar = 14.2, s = 2.7 A) (11.91, 16.49)...
In a dice game, you roll a fair die three times, independently. If you don’t roll any sixes, you lose 1 dollar. If you roll a six exactly once, you win one dollar. If you roll a six exactly twice, you win two dollars. If you roll a six all three times, you win k dollars. (A) Let k = 3. What is the expected value of the amount you would win by playing this game (rounded to the nearest...
in a game, you toss a fair coin and a fair six sided die. if you toss a heads on the coin and roll either a 3 or a 6 on the die, you win $30. otherwise, you lose $6. what is the expected profit of one round of this game
Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $9. If you roll a 3, 4 or 5, you win $4. Otherwise, you pay $2. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to decimal places where appropriate. Probability Distribution Table Х P(X) b. Find the expected profit. 5 (Round to the nearest cent) c. Interpret the...
Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $12. If you roll a 4 or 5, you win $1. Otherwise, you pay $2. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. Probability Distribution Table х P(X) b. Find the expected profit. $ (Round to the nearest cent)
Suppose that in a certain game you roll a die, and get winnings equal to $100 times the amount shown on the die. If you want to, you can roll again up to a total of three times. However, each time you roll again, you forfeit your previous winnings. You decide to take the following strategy: choose a number i, and if you ever get i or above, stop and collect your winnings, otherwise roll again. What is the value...
Suppose you are rolling a fair four-sided die and a fair six-sided die and you are counting the number of ones that come up. What is the probability that both die roll ones? What is the probability that exactly one die rolls a one? What is the probability that neither die rolls a one? What is the expected number of ones? If you did this 1000 times, approximately how many times would you expect that exactly one die would roll...
You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let N be the number of times the two dice have to be rolled before the game is decided. (d) Assume that you get paid $10 for winning in the first round, $1 for winning in any other round, and nothing otherwise. Compute your expected winnings. Answer: (d) You get paid $10 with...