Suppose you play a coin toss game in which you win $1 if a head appears and loses $1 if a tail appears. In the first 100 coin tosses, heads come up 46 times and tails come up 54 times. a) What percentage of times has heads come up in the first 100 tosses? What is your net gain or loss at this point? b) Suppose you toss the coin 200 more times( a total of 300 tosses), and at that point, heads have come up 47% of the time. Is this increase in the percentage of heads consistent with the law of large numbers? Explain. What is your net gain or loss at this point? 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? 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.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Suppose you play a coin toss game in which you win $1 if a head appears and loses $1 if a tail appears. In the first 100 coin tosses, heads come up 46 times and tails come up 54 times.
a) What percentage of times has heads come up in the first 100 tosses? What is your net gain or loss at this point?
b) Suppose you toss the coin 200 more times( a total of 300 tosses), and at that point, heads have come up 47% of the time. Is this increase in the percentage of heads consistent with the law of large numbers? Explain. What is your net gain or loss at this point?
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?
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.
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