StatTutor Lesson - The Idea of Probability

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      Question 1

      37

      Question 1.

      Suppose you want to know if a die is fair. How would you tell?

      A.
      B.
      C.
      D.

      Correct. If the die is fair, each face should occur about 1/6 of the time. This doesn’t mean that in a small number of tosses (or even a large number of tosses) that each face will occur exactly 1/6 of the time. With even 6000 tosses, we will only have an estimate of the true probability of each face of the die.
      Incorrect. If the die is fair, each face should occur about 1/6 of the time. This doesn’t mean that in a small number of tosses (or even a large number of tosses) that each face will occur exactly 1/6 of the time. With even 6000 tosses, we will only have an estimate of the true probability of each face of the die.
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      Applet

      64

      Applet

      190

      Question 2

      410

      Question 2.

      Which of the following could not be investigated with simulation?

      A.
      B.
      C.
      D.

      Correct. In order to study a process with simulation, it must have well-defined rules, just as the “Let’s Make a Deal” situation had. We could only simulate the amount spent on a date if we already knew the real average amount and how variable that amount is.
      Incorrect. In order to study a process with simulation, it must have well-defined rules, just as the “Let’s Make a Deal” situation had. We could only simulate the amount spent on a date if we already knew the real average amount and how variable that amount is.
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      Question 3

      460

      Question 3.

      Which of the following could be estimated with certainty?

      A.
      B.
      C.
      D.

      Correct. Playing the lottery each week is a long run situation. Both card and dice games are governed by probability in the long run, but we can’t say with any certainty what will happen on any one particular hand or turn. Getting stopped by police for speeding has many factors involved (weather, time of day, the particular stretch of road, etc.).
      Incorrect. Playing the lottery each week is a long run situation. Both card and dice games are governed by probability in the long run, but we can’t say with any certainty what will happen on any one particular hand or turn. Getting stopped by police for speeding has many factors involved (weather, time of day, the particular stretch of road, etc.).
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      Questions 4-5

      574

      Question 4.

      Is the question “Will I pass my statistics course?” uncertain or estimable for a randomly chosen student?

      A.
      B.

      Correct. For a randomly chosen student, we couldn’t answer the question without knowing more about his/her study habits, class attendance, and motivation to excel.
      Incorrect. For a randomly chosen student, we couldn’t answer the question without knowing more about his/her study habits, class attendance, and motivation to excel.
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      Question 6

      673

      Question 6.

      In 6000 simulated tosses of a die, you rolled a 6 1035 times. The estimated probability of a 6 for that die is (answer to 3 decimal places)

      Correct. The estimated probability of a 6 for this die is 1035/6000 = 0.1725, or 0.173 when rounded to three decimal places.
      Incorrect. The estimated probability of a 6 for this die is 1035/6000 = 0.1725, or 0.173 when rounded to three decimal places.
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