# Probability

posted by .

You and a friend play the following game: You pay your friend \$3 each turn and then flip a fair coin. It it’s tails, your friend pays you \$(2^n), where n is the number of times you’ve flipped the coin, and the game ends. If it’s heads, you have the choice of stopping and continuing. If you have m dollars to start with, and you play the game either until you win or until you have no money left, what will you win on the average?

Ah the good old St Petersburg Paradox.

Well, if you and your friend each have a infinite amount of money, then you can expect to win and infinite amount, on average.

## Similar Questions

1. ### Math

Would you be more likely to get at least 70% tails if you flip a fair coin 10 times or if you flip a fair coin 1000 times?
2. ### algebra

you and a friend oplay a game in which you each toss a coin. you score a point for each head and your friend scroes a point for each tail. the first person to score ten points wins. the score is 8 to 6 in your favor. describe a simulation …
3. ### math

You and your friend each have a coin. For each round, each of you flips your coin. If both coins show heads, your friend pays you \$3. If both show tails, your friend pays you \$1. If the coins don't match, you pay him \$2. Is this a …
4. ### statistics

A friend offers you the following game: You will roll 2 fair dice. If the sum of the two numbers obtained is 2,3,4,9,10,11,or 12 the friend will pay you \$20. However, if the sum of the two numbers is 5, 6,7, or 8, you pay your friend …
5. ### math

a fair coin is tossed in the air 4 times. if the coin lands heads up the first three tosses, what is the probability the coin will land heads up the fourth toss?
6. ### Statistics

Suppose Tori has an unfair coin which lands on Tails with probability 0.28 when flipped. If she flips the coin 10 times, find each of the following: Question 5 options: P(No more than 3 Tails) P(Exactly 1 Tail) P(At least 5 Tails) …
7. ### statistics

air coin is flipped 20 times. a. Determine the probability that the coin comes up tails exactly 15 times. b. Find the probability that the coin comes up tails at least 15 times. c. Find the mean and standard deviation for the random …
8. ### probability

You flip a fair coin (i.e., the probability of obtaining Heads is 1/2) three times. Assume that all sequences of coin flip results, of length 3, are equally likely. Determine the probability of each of the following events. {HHH}: …
9. ### Math-Probability

You have a friend who claims to be psychic. You don't believe this so you test your friend by flipping a coin 20 times and having him predict whether each flip is heads or tails. If you are right, and your friend is NOT psychic, the …
10. ### Math

You flip a coin 20 times and get tails 15 times you flip the coin 80 more times.what do you expect to happen to the experimental probability of getting tails as you increase the number of trials a. The experimental probability will …

More Similar Questions