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.
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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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.
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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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