# Chapter 1. The Idea of Probability

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0:37

### Question 1.1

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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1:04

3:10

6:50

### Question 1.2

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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7:40

### Question 1.3

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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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9:34

### Question 1.4

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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 1.5

Correct. By looking at the past history of grade distributions, it can be estimated which professor has higher pass rates.
Incorrect. By looking at the past history of grade distributions, it can be estimated which professor has higher pass rates.
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11:13

### Question 1.6

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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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