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A game involves selecting a card from a regular 52-card deck and tossing a coin. The coin is a fair coin and is equally likely to land on heads or tails. If the card is a face card, and the coin lands on Heads, you win $4 If the card is a face card, and the coin lands on Tails, you win $1 If the card is not a face card, you lose $1, no matter what the coin shows. Part (a) Find the expected value for this game (expected net gain or loss). (Round your answer to two decimal places.) $ Part (b) Explain what your calculations indicate about your long-term average profits and losses on this game. ○ The calculated value represents a fixed amount that your total money will change after each loss. The calculated value represents a fixed amount that your total money will change after each game. The calculated value represents the average amount per game that your total money will change over a large number of games. The calculated value represents the average amount per loss that your total money will change over a large number of games. Part (c) Should you play this game to win money? Yes, because the expected value indicates an expected average gain. No, because the expected value indicates an expected average loss.

A game involves selecting a card from a regular 52-card deck and tossing a coin. The coin is a fair coin and is equally likely to land on heads or tails. If the card is a face card, and the coin lands on Heads, you win $4 If the card is a face card, and the coin lands on Tails, you win $1 If the card is not a face card, you lose $1, no matter what the coin shows. Part (a) Find the expected value for this game (expected net gain or loss). (Round your answer to two decimal places.) $ Part (b) Explain what your calculations indicate about your long-term average profits and losses on this game. ○ The calculated value represents a fixed amount that your total money will change after each loss. The calculated value represents a fixed amount that your total money will change after each game. The calculated value represents the average amount per game that your total money will change over a large number of games. The calculated value represents the average amount per loss that your total money will change over a large number of games. Part (c) Should you play this game to win money? Yes, because the expected value indicates an expected average gain. No, because the expected value indicates an expected average loss.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CR: Chapter Review
Problem 72E
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A game involves selecting a card from a regular 52-card deck and tossing a coin. The coin is a fair coin and is equally likely to land on heads or tails. If the card is a face card, and the coin lands on Heads, you win $4 If the card is a face card, and the coin lands on Tails, you win $1 If the card is not a face card, you lose $1, no matter what the coin shows. Part (a) Find the expected value for this game (expected net gain or loss). (Round your answer to two decimal places.) $ Part (b) Explain what your calculations indicate about your long-term average profits and losses on this game. ○ The calculated value represents a fixed amount that your total money will change after each loss. The calculated value represents a fixed amount that your total money will change after each game. The calculated value represents the average amount per game that your total money will change over a large number of games. The calculated value represents the average amount per loss that your total money will change over a large number of games. Part (c) Should you play this game to win money? Yes, because the expected value indicates an expected average gain. No, because the expected value indicates an expected average loss.
Transcribed Image Text:A game involves selecting a card from a regular 52-card deck and tossing a coin. The coin is a fair coin and is equally likely to land on heads or tails. If the card is a face card, and the coin lands on Heads, you win $4 If the card is a face card, and the coin lands on Tails, you win $1 If the card is not a face card, you lose $1, no matter what the coin shows. Part (a) Find the expected value for this game (expected net gain or loss). (Round your answer to two decimal places.) $ Part (b) Explain what your calculations indicate about your long-term average profits and losses on this game. ○ The calculated value represents a fixed amount that your total money will change after each loss. The calculated value represents a fixed amount that your total money will change after each game. The calculated value represents the average amount per game that your total money will change over a large number of games. The calculated value represents the average amount per loss that your total money will change over a large number of games. Part (c) Should you play this game to win money? Yes, because the expected value indicates an expected average gain. No, because the expected value indicates an expected average loss.
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