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1- For example, suppose that you ask your father for some extra money. Instead of just giving you the money, he offers to flip a coin. If the coin lands "heads" – you win – and he will give you $20. If it lands “tails", you lose, and you receive nothing. In this example, we would say that the payout associated with the event that the coin lands "heads" is $20, and the payout associated with "tails" is $0. Before accepting your dad's offer, you turn to your mother and ask her for some extra money. Having overheard the conversation with your father, she makes a different offer. She will role a die, and give you $3 for every spot that turns up. (That is, if she rolls a 1, she will give you $3; if she rolls a 2, she will give you $6.00 (= 2 x $3.00), ... if she rolls a 6, she will give you $18 (= 6 x $3.00)). At this point you realize two things: First, you realize your parents are both very weird. Second, (since your mother and father won't both give you money) you realize that you need some way to compare the two offers. So which of these offers should you take? Which is the better offer? 2-A card is drawn at random from a deck consisting of cards numbered 2 through 10. A player wins 1 dollar if the number on the card is odd and loses 1 dollar if the number if even. What is the expected value of his winnings?

1- For example, suppose that you ask your father for some extra money. Instead of just giving you the money, he offers to flip a coin. If the coin lands "heads" – you win – and he will give you $20. If it lands “tails", you lose, and you receive nothing. In this example, we would say that the payout associated with the event that the coin lands "heads" is $20, and the payout associated with "tails" is $0. Before accepting your dad's offer, you turn to your mother and ask her for some extra money. Having overheard the conversation with your father, she makes a different offer. She will role a die, and give you $3 for every spot that turns up. (That is, if she rolls a 1, she will give you $3; if she rolls a 2, she will give you $6.00 (= 2 x $3.00), ... if she rolls a 6, she will give you $18 (= 6 x $3.00)). At this point you realize two things: First, you realize your parents are both very weird. Second, (since your mother and father won't both give you money) you realize that you need some way to compare the two offers. So which of these offers should you take? Which is the better offer? 2-A card is drawn at random from a deck consisting of cards numbered 2 through 10. A player wins 1 dollar if the number on the card is odd and loses 1 dollar if the number if even. What is the expected value of his winnings?

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.4: Expected Value
Problem 1E: If a game gives payoffs of $10 and $100 with probabilities 0.9 and 0.1, respectively, then the...
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1- For example, suppose that you ask your father for some extra money. Instead of just giving you the money, he offers to flip a coin. If the coin lands "heads" – you win – and he will give you $20. If it lands “tails", you lose, and you receive nothing. In this example, we would say that the payout associated with the event that the coin lands "heads" is $20, and the payout associated with "tails" is $0. Before accepting your dad's offer, you turn to your mother and ask her for some extra money. Having overheard the conversation with your father, she makes a different offer. She will role a die, and give you $3 for every spot that turns up. (That is, if she rolls a 1, she will give you $3; if she rolls a 2, she will give you $6.00 (= 2 x $3.00), ... if she rolls a 6, she will give you $18 (= 6 x $3.00)). At this point you realize two things: First, you realize your parents are both very weird. Second, (since your mother and father won't both give you money) you realize that you need some way to compare the two offers. So which of these offers should you take? Which is the better offer? 2-A card is drawn at random from a deck consisting of cards numbered 2 through 10. A player wins 1 dollar if the number on the card is odd and loses 1 dollar if the number if even. What is the expected value of his winnings?
Transcribed Image Text:1- For example, suppose that you ask your father for some extra money. Instead of just giving you the money, he offers to flip a coin. If the coin lands "heads" – you win – and he will give you $20. If it lands “tails", you lose, and you receive nothing. In this example, we would say that the payout associated with the event that the coin lands "heads" is $20, and the payout associated with "tails" is $0. Before accepting your dad's offer, you turn to your mother and ask her for some extra money. Having overheard the conversation with your father, she makes a different offer. She will role a die, and give you $3 for every spot that turns up. (That is, if she rolls a 1, she will give you $3; if she rolls a 2, she will give you $6.00 (= 2 x $3.00), ... if she rolls a 6, she will give you $18 (= 6 x $3.00)). At this point you realize two things: First, you realize your parents are both very weird. Second, (since your mother and father won't both give you money) you realize that you need some way to compare the two offers. So which of these offers should you take? Which is the better offer? 2-A card is drawn at random from a deck consisting of cards numbered 2 through 10. A player wins 1 dollar if the number on the card is odd and loses 1 dollar if the number if even. What is the expected value of his winnings?
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