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Probability
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 $8 If the card is a face card, and the coin lands on Tails, you win $2 If the card is not a face card, you lose $2, no matter what the coin shows. O Part (a) Find the expected value for this game (expected net gain or loss). (Round your answer to two decimal places.) $ O Part (b) Explain what your calculations indicate about your long-term average profits and losses on this game. O The calculated value represents the average amount per game that your total money will change over a large number of games. O The calculated value represents the average amount per loss that your total money will change over a large number of games. O The calculated value represents a fixed amount that your total money will change after each game. O The calculated value represents a fixed amount that your total money will change after each loss. O Part (c) Should you play this game to win money? O Yes, because the expected value indicates an expected average gain. O 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 $8 If the card is a face card, and the coin lands on Tails, you win $2 If the card is not a face card, you lose $2, no matter what the coin shows. O Part (a) Find the expected value for this game (expected net gain or loss). (Round your answer to two decimal places.) $ O Part (b) Explain what your calculations indicate about your long-term average profits and losses on this game. O The calculated value represents the average amount per game that your total money will change over a large number of games. O The calculated value represents the average amount per loss that your total money will change over a large number of games. O The calculated value represents a fixed amount that your total money will change after each game. O The calculated value represents a fixed amount that your total money will change after each loss. O Part (c) Should you play this game to win money? O Yes, because the expected value indicates an expected average gain. O No, because the expected value indicates an expected average loss.

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 61E: Roulette American roulette is a game in which a wheel turns on a spindle and is divided into 38...
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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 $8 If the card is a face card, and the coin lands on Tails, you win $2 If the card is not a face card, you lose $2, no matter what the coin shows. O Part (a) Find the expected value for this game (expected net gain or loss). (Round your answer to two decimal places.) 2$ Part (b) Explain what your calculations indicate about your long-term average profits and losses on this game. O 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. O The calculated value represents a fixed amount that your total money will change after each game. O The calculated value represents a fixed amount that your total money will change after each loss. O Part (c) Should you play this game to win money? O Yes, because the expected value indicates an expected average gain. O 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 $8 If the card is a face card, and the coin lands on Tails, you win $2 If the card is not a face card, you lose $2, no matter what the coin shows. O Part (a) Find the expected value for this game (expected net gain or loss). (Round your answer to two decimal places.) 2$ Part (b) Explain what your calculations indicate about your long-term average profits and losses on this game. O 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. O The calculated value represents a fixed amount that your total money will change after each game. O The calculated value represents a fixed amount that your total money will change after each loss. O Part (c) Should you play this game to win money? O Yes, because the expected value indicates an expected average gain. O No, because the expected value indicates an expected average loss.
Expert Solution
Step 1

Given that,  a game involves selecting a cardbfrom a regular 52 card deck annd tossing a coin.

  • If the card is a face card, and the coin lands on Heads, you win $ 8
  • If the card is a face card, and the coin lands on Tails, you win $ 2
  • If the card is not a face card, you loss $ 2, no matter what the coin shows.

 

We need to find the expected value of this game.

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