At a charity event, a player rolls a pair of dice. If the player roles a...

At a charity event, a player rolls a pair of dice. If the player roles a pair (same number on each die), the player wins $10. If the two are exactly one number a part (like a five and a six), the player wins $6. IF the player roles a one and a six, they win $15. Otherwise, they lose. If it cost $5 to play, find the expected value. Write a complete sentence to explain what your answer means without words "Expected value". Show all work for full credit including the probability distribution.

Solutions

Expert Solution

Pay: $5 to play

X = the number of dollars won or lost.

List the values that X may take on is X ∈ {10, 6, 15,0}

Construct a PDF

P(X = 10) = 6/36 = 1/6 (There are 6 different ways in which player can roll same number on each die. Total number of combinations possible is 6*6 = 36)

P(X = 6) = 10/36 = 5/18 (There are 10 different ways in which player can roll die such that two are exactly one number apart. Total number of combinations possible is 6*6 = 36)

P(X = 15) = 2/36 = 1/18 (There are 2 different ways in which player can roll a one and a six. Total number of combinations possible is 6*6 = 36)

P(X = 0) = 18/36 = 1/2 (There are 18 different ways in which player can lose)

Expected Value = 10*1/6 + 6*5/18 + 15*1/18 + 0*1/2 - 5

Expected Value = -0.8333

Because the expected value is a negative answer, we'd say that the game is NOT fair. In the long run, players of this game will lose money.

milcah answered 10 months ago

Next > < Previous

Related Solutions

In the game of Lucky Sevens, the player rolls a pair of dice. If the dots...

In the game of Lucky Sevens, the player rolls a pair of dice. If the dots add up to 7, the player wins $4; otherwise, the player loses $1. Suppose that, to entice the gullible, a casino tells players that there are lots of ways to win: (1, 6), (2, 5), and so on. A little mathematical analysis reveals that there are not enough ways to win to make the game worthwhile; however, because many people’s eyes glaze over at...

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.

In a dice game a player first rolls two dice. If the two numbers are l...

In a dice game a player first rolls two dice. If the two numbers are l ≤ m then he wins if the third roll n has l≤n≤m. In words if he rolls a 5 and a 2, then he wins if the third roll is 2,3,4, or 5, while if he rolls two 4’s his only chance of winning is to roll another 4. What is the probability he wins?

Shandelle rolls a pair of fair dice and sums the number of spots that appear on...

Shandelle rolls a pair of fair dice and sums the number of spots that appear on the up faces. She then flips a fair coin the number times associated with the sum of the spots. For example, if she rolled a 3 and a 4, then she flips the fair coin 7 times. If the coin flipping part of the random experiment yielded an equal number of heads and tails, find the probability that she rolled an 8 on the...

PROGRAMMING IN C-DICE GAME Q1. A player rolls two dice at the same time. Each die...

PROGRAMMING IN C-DICE GAME Q1. A player rolls two dice at the same time. Each die has six faces, which contain 1, 2, 3, 4, 5 and 6 spots. After the dice have come to rest, the sum of the spots on the two upward faces is calculated. (i) If the sum is 2 or 10 on the first throw, the player wins. (ii) If the sum is 3, 7 or 12 on the first throw, the player loses. (iii)...

You are rolling a pair of balanced dice in a board game. Rolls are independent. You...

You are rolling a pair of balanced dice in a board game. Rolls are independent. You land in a danger zone that requires you to roll doubles (both faces show the same number of spots) before you are allowed to play again. 1. What is the probability of rolling doubles on a single toss of the dice? A) 25/36 B) 5/36 C) 1/6 D) 1/36 2. What is the probability that you do not roll doubles on the first toss,...

Alice rolls a pair of fair six-sided dice until a sum of 6 appears for the...

Alice rolls a pair of fair six-sided dice until a sum of 6 appears for the first time. Independently, Bob rolls two fair six-sided dice until he rolls a sum 7 for the first time. Find the probability that the number of times Alice rolls her dice is equal to or within one of the number of times Bob rolls his dice.

A game works as follows: the player rolls one dice once (let's call it ''n'') and...

A game works as follows: the player rolls one dice once (let's call it ''n'') and then he rolls it second time (let's call this second roll "m'') and receives nm points . A)What is the probability that n = 1 knowing that the player has received more than 20 points. b) What is the probability that m = 1 knowing that the player has received more than 20 points. c) (What is the probability that the player receives more...

In the game of craps, a player (known as the shooter) rolls two fair six-sided dice....

In the game of craps, a player (known as the shooter) rolls two fair six-sided dice. The shooter immediately loses if the sum of the dice is 2, 3, or 12 and immediately wins if the sum of the dice is 7 or 11 on the first roll. If the sum is anything else (4, 5, 6, 8, 9, or 10), that number becomes the point and the shooter rolls again. The shooter now wins by rolling that same point...

PLEASE USE PYTHON THANK YOU In the game of Lucky Sevens, the player rolls a pair...

PLEASE USE PYTHON THANK YOU In the game of Lucky Sevens, the player rolls a pair of dice. If the dots add up to 7, the player wins $4; otherwise, the player loses $1. Suppose that, to entice the gullible, a casino tells players that there are many ways to win: (1, 6), (2, 5), and soon. A little mathematical analysis reveals that there are not enough ways to win to make the game worthwhile; however, because many people's eyes...

Subjects