LUll Ulldatloh of data from polls across the 50 states. In what way are these po
ID: 3174073 • Letter: L
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LUll Ulldatloh of data from polls across the 50 states. In what way are these polls likely to be independent tri als? Why could someone argue that they are not truly independent trials? 5.50 Independent or dependent trials and probability: Gamblers often falsely predict the outcome of a future trial based on the outcome of previous trials. When trials are independent, the outcome of a future trial cannot be predicted based on the outcomes of previ ous trials. For each of the following examples, (1) state whether the trials are independent or dependent and (2) explain why. In addition, (3) state whether it is possible that the quote is accurate or whether it is defi- nitely fallacious, explaining how the independence or dependence of trials influences accuracy. a. You are playing Monopoly and have rolled a pair of sixes in 4 out of your last 10 rolls of the dice. You say, "Cool. I'm on a roll and will get sixes again b. You are an Ohio State University football fan and are sad because the team has lost two games in a row. You say, "That is really unusual; the Buckeyes are doomed this season. That's what happens with lots of early-season injuries."Explanation / Answer
(a) For monopoly all the trials are independent, hence the number of sixes in previous trials does not indicate the outcome in the future trials. So the player may or may not get sixes next. Hence the quote is neither accurate nor definitely fallacious.
(b) The trials (each match) is dependent. Since the team is playing with a fixed set of players in each match and their fitness and ability is not independent in each match. Hence the probability of winning a match is dependent on results of previous matches. The quote is not definite fallacious but also may not be accurate. However, it may have some truth to it, since early season injuries affect the season's performances in a malicious way.
(c) The trials are dependent. Since the probability of a failure in depends on the goodness of the engine. The tuning up last week will tend to heal the engine and one can expect that this is reflected in this week's strong performance. Hence the law of large numbers with probability of failure equal to half is not applicable. Rather we can say that the probability of failure has decreased with the tune up. One should, however, also keep in mind that this does not mean that there will be surely success or failure. Hence I think that the quote is fallacious.
(d) The trails are independent. Since each of the stockings are bought from different stores and potentially made in different places at different times -there is no way that performance of one can determine of performance of the other. Hence next day's stocking may or may not fail. The statement is fallacious.
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