This is lab activity 9, "Simulation and the law of large numbers

Select the best answer for each question. An answer may be used once, more than once or not at all. v What does the horizontal line represent? v What does the line that moves up or down represent? v How does the graph relate to the Law of Large Numbers? My friend, Kevin, thinks he is psychic. He believes he can predict the correct outcome when a coin is tossed 75% of the time. If I pay $3 to play this game, Kevin will pay me $5 if he is wrong. What is the probability model for the amount won in this game? My friend, Kevin, thinks he is psychic. He believes he can predict the correct outcome when a coin is tossed 75% of the time. If I pay $3 to play this game, Kevin will pay me $5 if he is wrong. What is the expected winnings for this game? My friend, Kevin, thinks he is psychic. He believes he can predict the correct outcome when a coin is tossed 75% of the time. If I pay $3 to play this game, Kevin will pay me $5 if he is wrong. How much would I win/lose if I played this game 50 times? My friend, Kevin, thinks he is psychic. He believes he can predict the correct outcome when a coin is tossed 75% of the time. If I pay $3 to play this game, Kevin will pay me $5 if he is wrong. If Kevin is not psychic, what is the probability model for the amount won in this game? My friend, Kevin, thinks he is psychic. He believes he can predict the correct outcome when a coin is tossed 75% of the time. If I pay $3 to play this game, Kevin will pay me $5 if he is wrong. If Kevin is not psychic, what is the expected winnings for this game? A, Amount E. Amount Probability $0 .5 $5 .5 B. $62.50. But since it would cost me $150 to play 50 games, I would actually lose $87.50. C. $1.25 D,The probabilities from the third row of the table. Probability $0 .75 $5 .25 F. $187.50. But since it would cost me $150 to play 50 games, I would only gain $37.50. G,The long run probability of tossing heads on a coin. H. $3.75 |_ Amount Probability $0 .25 $5 .75 $2.50 K. As you look at the graph from left to right, the line that moves up and down (the actual probabilities) gets closer and closer to the horizontal line (the long run probability) as the sample size gets larger which is what the Law of Large Numbers states. L. $125. But since it would cost me $150 to play 50 games, I would actually lose $25. Select the best answer for each question. Answers may be used once, more than once or not at all. . v Are the outcomes of tossing a two-sided coin independent? Why or why not? . v What is the long run probability of tossing heads on a two-sided coin? - v What do you notice about the calculated probabilities as you read the third row of the table from left to right? Describe the trend you see. . v How does the law of large numbers explain this observation? US 7\" A. Yes, a coin has no memory. It cannot remember how it landed on a previous toss. It will behave the same way on each toss. So the outcome of this toss is not affected by the outcome of the previous toss. . 0.25 . No, the outcomes of tossing a two-sided coin are not independent because the previous toss would affect the outcome ofthe next outcome. .There is no trend when observing the probabilities in the third row of the table from left to right. . The law of large numbers states that if a random phenomenon with numerical outcomes (like tossing a coin) is repeated many times independently, the probability of the actually observed outcomes (the third row of the table) approaches the expected value (the long run probability of tossing a coin). 0.5 .The law of large numbers does not apply to this situation. .As you observe the probabilities from left to right in the third row of the table the values get closer and closer to the long-run probability with smaller and smaller variations