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Chapter 15 Probability Rules!

Chapter 15 Probability Rules!. General Addition Rule Conditional Probability. Recall…. for any Random phenomenon each trial generates an outcome An event is a set of outcomes The collection of all possible outcomes is called the SAMPLE SPACE (S). Sample Space.

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Chapter 15 Probability Rules!

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  1. Chapter 15Probability Rules! General Addition Rule Conditional Probability

  2. Recall… • for any Random phenomenon • each trial generates • an outcome • An event is a set of outcomes • The collection of all possible outcomes is called the SAMPLE SPACE (S)

  3. Sample Space List the sample space and tell whether you think they are equally as likely • Toss 2 coins; record the order of heads and tails • A family has 3 children; record the number of boys • Flip a coin until you get a head or 3 consecutive tails • Roll two dice; record the larger number

  4. Drawing Venn Diagrams Real Estate ads suggest that 64% of homes for sale have garages, 21% have swimming pools, and 17% have both features. What is the probability that a home for sale has • a pool or a garage? • neither a pool nor a garage? • a pool but no garage?

  5. General Addition Rule • Does NOT require disjoint events

  6. Conditional Probabilities A Gallup survey of June 2004 asked 1005 U.S. adults who they think better fits their idea of what a first lady should be, Laura Bush or Hillary Clinton. • What is the probability that the person thought Laura Bush best fits their first lady ideals? • What is the probability that the person is younger than 50? • What is the probability that the person is younger than 50 and thinks Clinton is a better fit? • What is the probability that the person is younger than 50 or thinks Clinton is a better fit?

  7. Conditional Probability “The probability of B given A”

  8. Conditional Probabilities You draw a card at random from a standard deck of 52 cards. Find the following conditional probabilities. • the card is a heart, given that it is red. • the card is red, given that it is a heart • the card is an ace, given that it is red • the card is a queen given that it is a face card

  9. Chapter 15 Probability Rules! *General Multiplication Rule *Testing for Disjoint/Independence *Probability Tables *Tree Diagrams

  10. General Multiplication Rule ** when A and B are INDEPENDENT, then ** • When A and B are NOT independent, then Which event you define as A or B does not matter

  11. How do we know if two event are INDEPENDENT?? If P(B|A) = P(B), then A and B are independent Example: Is good grades as a goal independent of gender??

  12. Events can NOT be disjoint AND independent • Consider • Event A = {making the team} • Event B = {not making the team}

  13. Probability Tables Construct a probability table with the given information. Suppose 78% of DUI suspects are given a breath test, 36% a blood test, and 22% of DUI suspects receive both tests.

  14. Are giving a DUI suspect a blood test and a breath test mutually exclusive (disjoint)? • Are giving the 2 tests independent?

  15. Drawing without Replacing • Suppose you are drawing cards from a standard deck. • What is the probability you will draw 3 spades in a row??

  16. Data on College Binge Drinking • 44% binge drink • 37% drink moderately • 19% abstain completely • Of those who binge drink: 17% car accidents • Of those who drink moderately: 9% car accidents FIND: P(college student who binge drinks and has been involved in a car accident)

  17. Tree Diagram • shows sequence of events • make when using GMR • covers all possible outcomes • probabilities should add up to 1

  18. Reversing the Conditions • What is the probability the student is a binge drinking given they were in an accident. • Tree Diagram given P(accident|binge drinker) • Use the tree to find P(binge|accident)

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