Suppose you toss a fair coin 100 times, getting 42 heads and 58 tails, which is

Question

Suppose you toss a fair coin 100 times, getting 42 heads and 58 tails, which is 16 more tails than heads. Complete parts (a) through (c) below. a. Explain why, on your next toss, the difference between the numbers of heads and tails is as likely to grow to 17 as it is to shrink to 15. Choose the correct answer below. A. On every toss, there is a 0.5 probability that it will land on tails. Therefore, half of the time it will land on tails. The difference is likely to change half of the time. O B. On every toss, there is a 0.5 probability that it will land on heads. Therefore, half of the time it will land on heads. The difference is likely to change half of the time. C. On every toss, it is just as likely to land on heads as it is to land on tails. If you toss a head, the difference becomes 15. If you toss a tail, the difference becomes 17. ( D. On every toss, it is just as likely to land on heads as it is to land on tails. If you toss a tail, the difference becomes 15. lf you toss a head, the difference becomes 17. b. Extend your explanation from part (a) to explain why, if you toss the coin 1000 more times, the final difference between the numbers of heads and tails is as likely to be larger than 16 as it is to be smaller than 16 Choose the correct answer below. A. On each toss, the difference in heads and tails is not likely to increase or decrease. However, after 1000 tosses, the difference is equally likely to be greater than 16 or less than 16. O B. On each toss, the difference in heads and tails is equally likely to increase or decrease-Ater 1000 tosses, the difference is equally likely to be greater than 16 or less than 16. C. On each toss, the difference in heads and tails is more likely to increase. After 1000 tosses, the difference is equally likely to be greater than 16 or less than 16. D. On each toss, the difference in heads and tails is more likely to decrease. After 1000 tosses, the difference is equally likely to be greater than 16 or less than 16 C. Suppose you are betting on heads with each coin toss. After the first 100 tosses, you are well on the losing side. Explain why, if you continue to bet, you will most likely remain on the losing side. How is this answer related to the gambler's fallacy? Choose the correct answer below O A. According to the law of large numbers, the probability of losing will become closer to the probability of P(A). The results of repeated tosses do not depend on the results of earlier tosses. O B. Once you have fewer heads than tails, the deficit of heads is likely to remain. A streak of bad luck does not mean that a person is due for a streak of good luck. O C. The expected value decreases with each toss. Therefore, it is likely that the losing streak will continue. Most gamblers keep trying because they think that they are due for a win sometime soon. O D. The probability of winning will always be 50%. There is no such thing as good luck in gambling because the chances are always predicted by numbers

Explanation / Answer

a) C option

As probability of getting a head or a tail is same.

b) B option

Same logic as in part a)

c) The gambler's fallacy, also known as the Monte Carlofallacy or the fallacy of the maturity of chances, is the belief that, if something happens more frequently than normal during some period, it will happen less frequently in the future.

A option

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