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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 34 times and tails comes up 66 times. Answer parts (a) through (d) below. a. What percentage of times has heads come up in the first 100 tosses? 34% What is your net gain or loss at this point? Select the correct choice and fill in the answer box to complete your choice. A. You have lost $ 32. (Type an integer.) B. You have gained $ nothing. (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. A. The change is 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 the percentage is low the first 100 trials, it has to be higher the next 200 trials to even out. C. 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%. D. The change is not consistent with the law of large numbers, because the trials are not independent. What is your net gain or loss at this point? Select the correct choice and fill in the answer box to complete your choice. A. You have gained $ nothing. (Type an integer.) B. You have lost $ nothing. (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 choice and fill in the answer box to complete your choice. A. You would need to toss nothing heads. This is likely because so few heads have been tossed so far. B. You would need to toss nothing heads. This is unlikely as it is far from the expected number of heads. C. You would need to toss nothing heads. This is likely because it is close to 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. A. This illustrates the gambler's fallacy because eventually there will be a winning streak. B. 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. C. This illustrates the gambler's fallacy because the number of heads cannot be under 50% all the time. D. This illustrates the gambler's fallacy because the probability of getting heads is always 0.5.

          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 34 times and tails comes up 66 times. Answer
parts (a) through (d) below. a. What percentage of times has
heads come up in the first 100 tosses? 34% What is your net gain
or loss at this point? Select the correct choice and fill in the
answer box to complete your choice. A. You have lost $ 32. (Type
an integer.) B. You have gained $ nothing. (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. A. The change is 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 the percentage is low the
first 100 trials, it has to be higher the next 200 trials to even
out. C. 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%. D. The change is not consistent with the law
of large numbers, because the trials are not independent. What is
your net gain or loss at this point? Select the correct choice and
fill in the answer box to complete your choice. A. You have gained
$ nothing. (Type an integer.) B. You have lost $ nothing.
(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 choice and fill in the answer box to
complete your choice. A. You would need to toss nothing heads. This
is likely because so few heads have been tossed so far. B. You
would need to toss nothing heads. This is unlikely as it is far
from the expected number of heads. C. You would need to toss
nothing heads. This is likely because it is close to 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. A. This illustrates the gambler's fallacy because
eventually there will be a winning streak. B. 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. C. This
illustrates the gambler's fallacy because the number of heads
cannot be under 50% all the time. D. This illustrates the
gambler's fallacy because the probability of getting heads is
always 0.5.

Added by David S.

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