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Solutions for Session 8, Part A
See solutions for Problems: A1 | A2 | A3 | A4 | A5
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Problem A1 | |
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Answers will vary. Some everyday uses of probability are predicting the weather, deciding which road is likely to have the least amount of traffic, and choosing a restaurant on the basis of how long you think the wait will be. Some mathematical uses include the probability of rolling a six on a die, the probability of tossing a coin and getting "heads," and the probability of 1-2-3 coming up as the daily lottery number.
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Problem A2 | |
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Statistical uses of probability include the probability that the estimate of a mean is accurate (this is known as a confidence interval). Places where probability uses statistics include taking experimental data and trying to create exact probabilities to match your data set.
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Problem A3 | |
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A "random" event is entirely up to chance; there is no skill involved. A random event might be what appears as the top card after a thorough shuffling of a deck of cards. Most events are not random; for example, answering a question correctly on a test may happen randomly (as a guess) but usually is a result of skill.
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Problem A4 | |
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You might look at your average score and determine whether your average score is improving over time. For example, if you played Push Penny 20 times a day for several days, you could compare your average first day's score to your average last day's score and see if there was any improvement.
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Problem A5 | |
a. | Answers will vary. |
b. | Answers will vary. |
c. | One example of such a game is a game where you shuffle a deck of cards thoroughly and then try to guess the suit of the top card. Since the top card is completely random, there is no way to develop your skill in correctly guessing the suit of the card (without cheating or using ESP!). The card game War is another example. |
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