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3. Betty is playing a game with a fair die. If she rolls a prime number, she scores 10 times the number rolls. If she rolls a composite number, she scores 5 times the number rolls. If she rolls anything else, she scores the number rolled. What score should Betty expect on average?

3. Betty is playing a game with a fair die. If she rolls a prime number, she scores 10 times the number rolls. If she rolls a composite number, she scores 5 times the number rolls. If she rolls anything else, she scores the number rolled. What score should Betty expect on average?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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MATH 0332/1332 Assignment 6.4 Mathematical Expectation (Expected Value) Create a probability distribution for the given scenario. Then use that probability distribution to calculate the mathematical expectation (expected value) and answer any other questions. 1. Find the expected number of tails obtained when tossing three coins. [1.5tails 2. The first team to win four games in the World Series wins the championship. In 40 World Series events, there have been 8 times where four games were needed to decide the series, 7 times when five games were needed to decided the series, 9 times when six games were needed to decide the series, and 16 times where all seven games were needed to decide the series. Find the expected number of games played in the World Series. 5.825games/353 3. Betty is playing a game with a fair die. If she rolls a prime number, she scores 10 times the number rolls. If she rolls a composite number, she scores 5 times the number rolls. If she rolls anything else, she scores the number rolled. What score should Betty expect on average? 4. The spinner below is being used in a casino game. The spinner has eight equal sectors. Each sector is a certain color (P = purple, R = red, Y = yellow, and B = blue). You must pay $5 to play the game. If the arrow lands on purple, the payoff is zero. If the arrow lands on red, the payoff is $3. If the arrow lands on yellow, the payoff is $6. If the arrow lands on blue, the payoff is $16. If you play this game, what is your expected net winning?\= -$0 5 O -5 3-5 6-5 |lb-5 + winning-$5/-28 $1 R EG): -53) -2G)+1F R Y 3. Y of P = -$0.15 5. An insurance company will insure a $130,000 home for its total value for an annual premium of $950. If the company spends $30 per year to service such a policy, the probability of total loss for such a home in a given year is 0.002 and a partial loss of $5000 is 0.005. If you assume that either total loss, $5000 partial loss or no loss will occur, what is the company's expected annual gain (or profit) on such a policy? 6. A college foundation raises funds by selling raffle tickets for a new car worth $45,000. If 800 tickets are sold for $100 each, determine: The expected net winnings of a person buying one of the tickets. a. b. The total profit for the foundation, assuming that the car was donated. The total profit for the foundation, assuming that it had to purchase the car. с. ード」A 2/8
Transcribed Image Text:MATH 0332/1332 Assignment 6.4 Mathematical Expectation (Expected Value) Create a probability distribution for the given scenario. Then use that probability distribution to calculate the mathematical expectation (expected value) and answer any other questions. 1. Find the expected number of tails obtained when tossing three coins. [1.5tails 2. The first team to win four games in the World Series wins the championship. In 40 World Series events, there have been 8 times where four games were needed to decide the series, 7 times when five games were needed to decided the series, 9 times when six games were needed to decide the series, and 16 times where all seven games were needed to decide the series. Find the expected number of games played in the World Series. 5.825games/353 3. Betty is playing a game with a fair die. If she rolls a prime number, she scores 10 times the number rolls. If she rolls a composite number, she scores 5 times the number rolls. If she rolls anything else, she scores the number rolled. What score should Betty expect on average? 4. The spinner below is being used in a casino game. The spinner has eight equal sectors. Each sector is a certain color (P = purple, R = red, Y = yellow, and B = blue). You must pay $5 to play the game. If the arrow lands on purple, the payoff is zero. If the arrow lands on red, the payoff is $3. If the arrow lands on yellow, the payoff is $6. If the arrow lands on blue, the payoff is $16. If you play this game, what is your expected net winning?\= -$0 5 O -5 3-5 6-5 |lb-5 + winning-$5/-28 $1 R EG): -53) -2G)+1F R Y 3. Y of P = -$0.15 5. An insurance company will insure a $130,000 home for its total value for an annual premium of $950. If the company spends $30 per year to service such a policy, the probability of total loss for such a home in a given year is 0.002 and a partial loss of $5000 is 0.005. If you assume that either total loss, $5000 partial loss or no loss will occur, what is the company's expected annual gain (or profit) on such a policy? 6. A college foundation raises funds by selling raffle tickets for a new car worth $45,000. If 800 tickets are sold for $100 each, determine: The expected net winnings of a person buying one of the tickets. a. b. The total profit for the foundation, assuming that the car was donated. The total profit for the foundation, assuming that it had to purchase the car. с. ード」A 2/8
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