Suppose you play a coin toss game in which you win​ $1 if a head appears and lose $1 if a tail appears. In the first 100 coin​ tosses, heads comes up 36 times and tails comes up 64 times. a. What percentage of times has heads come up in the first 100​ tosses? Answer 1 Question 5%

What is your net gain or loss at this​ point? Select the correct choice and fill in the answer box to complete your choice. You have Answer 2 Question 5 $Answer 3 Question 5. (Type an integer)

b. Suppose you toss the coin 200 more times​ (a total of 300​ tosses), and at that point heads has come up 37​% of the time. Is this change in the percentage of heads consistent with the law of large​ numbers? Explain. Multiple choice 1 Question 5 A. The change is not consistent with the law of large numbers​ because, as the number of trials​ increases, the proportion should grow closer to​ 50%. B. The change is consistent with the law of large numbers​ because, as the number of trials​ increases, the proportion should grow closer to​ 50%. C. The change is not consistent with the law of large​ numbers, because the trials are not independent. D. The change is consistent with the law of large numbers. Because the percentage is low the first 100​ trials, it has to be higher the next 200 trials to even out.

What is your net gain or loss at this​ point? Select the correct choice and fill in the answer box to complete your choice. You have Answer 4 Question 5 $Answer 5 Question 5. (Type an integer)

c. How many heads would you need in the next 100 tosses in order to break even after 400​ tosses? Is this likely to​ occur? Select the correct choices and fill in the answer box to complete your choice. You would need to toss Answer 6 Question 5 heads. This is Answer 7 Question 5 because it is Answer 8 Question 5 from the expected number of heads.

d. Suppose​ that, still behind after 400​ tosses, you decide to keep playing because you are due for a winning streak. Explain how this belief would illustrate the​ gambler's fallacy. Multiple choice 2 Question 5 A. This illustrates the​ gambler's fallacy because eventually there will be a winning streak. B. This illustrates the​ gambler's fallacy because the number of heads cannot be under​ 50% all the time. C. This illustrates the​ gambler's fallacy​ because, due to the law of large​ numbers, the probability of getting heads must now be more than 0.5. D. This illustrates the​ gambler's fallacy because the probability of getting heads is always 0.5