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Chapter 13 Probability Rules

Chapter 13 Probability Rules. In this chapter we look at some general rules about probability and some special diagrams that will aid us in using these rules correctly. For any two events E & F : If E and F are disjoint :. Addition Rule.

jacqueline-bowers
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Chapter 13 Probability Rules

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  1. Chapter 13Probability Rules In this chapter we look at some general rules about probability and some special diagrams that will aid us in using these rules correctly.

  2. For any two events E & F: If E and F are disjoint: Addition Rule

  3. For any two events E & F, the conditional probability that event E occurs given that event F occurs is: This is the probability that event Eoccurs when we know that event F will definitely occur. Conditional Rule

  4. For any two events E & F: If E and F are independent: Events E and F are independent if Multiplication Rule

  5. Remembering how and when to use each of these rules is not always easy. Using appropriate graphical representations of the situation (Venn diagrams or Tree diagrams) can help with this. We will look at this through examples. Then, the only formula we really have to remember for more complex scenarios is the conditional probability formula. My Thoughts

  6. Employment data at a large company reveals that 72% of the workers are married, 44% have college degrees, and that half the college grads are married. A single person is selected at random from this company. Find: (a)P(person is not married nor a college grad) (b)P(person is married but not a college grad) (c)P(person is married or a college grad but not both) (d)P(person is a college grad given that (s)he is married) Example 1

  7. Police report that 78% of drivers pulled over are given a breath test, 36% a blood test, and 22% are given both. A random person that has been pulled over by the police is selected. Define A = person is given a breath test and define B = person is given a blood test. Find and interpret the following probabilities: (a) (b) (c) (d) (e) Example 2

  8. According to a certain study, 44% of college students engage in binge drinking, 37% drink moderately, and 19% abstain from drinking. Another study found that among binge drinkers, 17% have been responsible for an alcohol related accident and 9% of non-binge drinkers (moderate drinkers) have been responsible for an alcohol related accident. A college student is selected at random. Find the following probabilities: (a) P(was responsible for an alcohol related accident) (b) P(was responsible for an alcohol related accident | is a binge drinker) (c) P(has not been responsible for an alcohol related accident) (d) P(is a moderate drinker | has not been responsible for an alcohol related accident) (e) P(is a binge drinker | has been responsible for an alcohol related accident) Example 3

  9. A study showed that in 77% of all accidents, the driver was wearing a seatbelt. Of these, 92% escaped serious injury, but only 63% of drivers without seatbelts escaped serious injury. A person involved in an accident is randomly selected. Define S =(s)he wore a seatbelt and define E = (s)he escaped serious injury. Find and interpret the following: (a) (b) (c) Example 4

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