Question

In: Statistics and Probability

A gambler plays a dice game where a pair of fair dice are rolled one time...

A gambler plays a dice game where a pair of fair dice are rolled one time and the sum is recorded. The gambler will continue to place $2 bets that the sum is 6, 7, 8, or 9 until she has won 7 of these bets. That is, each time the dice are rolled, she wins $2 if the sum is 6, 7, 8, or 9 and she loses $2 each time the sum is not 6, 7, 8, or 9 and she keeps playing like this until she's won 7 times.

a. What's the probability she places a total of 12 bets?

b. What's her expected winnings when she stops?

Solutions

Expert Solution

orchestra answered 1 year ago
Next > < Previous

Related Solutions

In the carnival game​ Under-or-Over-Seven, a pair of fair dice is rolled​ once, and the resulting...
In the carnival game​ Under-or-Over-Seven, a pair of fair dice is rolled​ once, and the resulting sum determines whether the player wins or loses his or her bet. For​ example, using method​ one, the player can bet $2.00 that the sum will be under​ 7, that​ is, 2,​ 3, 4,​ 5, or 6. For this​ bet, the player wins $2.00 if the result is under 7 and loses $2.00 if the outcome equals or is greater than 7.​ Similarly, using...
In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting...
In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, the player can bet $1 that the sum will be under 7—that is, 2, 3, 4, 5, or 6. For this bet, the player wins $1 if the result is under 7 and loses $1 if the outcome equals or is greater than 7. Similarly, the player can bet $1...
A pair of fair dice are rolled once. Suppose that you lose $7 if the dice...
A pair of fair dice are rolled once. Suppose that you lose $7 if the dice sum to 3 and win $12 if the dice sum to 4 or 12. How much should you win or lose if any other sum turns up in order for the game to be fair. I got a negative answer and im not sure thats correct.
A pair of fair dice is rolled. Find the expected value of the (a) Smaller (b)...
A pair of fair dice is rolled. Find the expected value of the (a) Smaller (b) Larger of the two upturned faces. (If both dice show the same number, then take this to be the value of both the smaller and the larger of the upturned faces.)
A pair of dice is rolled and the sum of the dice is recorded, determine the...
A pair of dice is rolled and the sum of the dice is recorded, determine the probability that: a) The sum is greater than 5 given the first dice is a 4. b) The sum is greater than 9 given the second dice is a 6. c)The sum is even given the second dice is a 4 d) The sum is odd given the first dice is a 3 e) A double is rolled given neither dice is a 4...
Suppose that a game of chance is played with a pair of fair 10-sided dice (with...
Suppose that a game of chance is played with a pair of fair 10-sided dice (with the sides numbered 1 to 10). In the game, you can pick any number from 1 to 10 and the two dice are then “rolled” in a cage. If $1 is bet and exactly one of the number that you picked is rolled you win $1, and if both of the dice are the number that you picked you win $20 (in each of...
A pair of dice are rolled. Let A be the event as “the first dice roll...
A pair of dice are rolled. Let A be the event as “the first dice roll is 3” and event B as “the second dice roll is 4”. Let event C be as “the sum of the dice rolls are 7.” a) Show that A and B are independent, that A and C are independent, and that B and C are independent. b) Show that A, B, and C are not mutually independent.
What is the probability that at least one of a pair of fair dice lands of...
What is the probability that at least one of a pair of fair dice lands of 5, given that the sum of the dice is 9?
Consider the game consisting of rolling a pair of fair 6-sided dice and recording the sum....
Consider the game consisting of rolling a pair of fair 6-sided dice and recording the sum. It will cost you $1 to play the game. If the sumis less than 5, then you will win $3. However, you do not get your $1 back so your profit is $2. If you roll a sum of exactly8, thenyou will win $4. However, you do not get your $1 back so your profit is $3. Otherwise, you lose your $1. A.What is...
a pair of dice are rolled and if the sum is a 5, Derek gets a...
a pair of dice are rolled and if the sum is a 5, Derek gets a point; if the sum is a 6, Ker gets a point; if the sum is a 7, Gary gets a point. if the sum is some other value, no one gets a point. (a) if the dice are rolled until Gary gets 4 points, find the probability Derek gets exactly 2 points. (b) if the dice are rolled until Gary gets 4 points, find...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT