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AP Statistics Section 6.3 B Conditional probability

AP Statistics Section 6.3 B Conditional probability. Slim considers himself a pretty good poker player, at least when he is the only one playing. He has been dealt 4 cards and wishes to know the probability that his 5 th card will be an ace. Can we figure this probability ?.

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AP Statistics Section 6.3 B Conditional probability

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  1. AP Statistics Section 6.3 BConditional probability

  2. Slim considers himself a pretty good poker player, at least when he is the only one playing. He has been dealt 4 cards and wishes to know the probability that his 5th card will be an ace. Can we figure this probability? Not without knowing what the first four cards were

  3. Find P(5th card is an ace) if his first 4 cards aretwo 3s, a 7 and a jack

  4. Find P(5th card is an ace) if his first 4 cards aretwo 3s, a 7 and an ace.

  5. The probability we assign to an event can change if we know that some other event has occurred.

  6. When a probability is based on the knowledge of a previous event it is called

  7. The notation for conditional probability is _______. This notation is read:

  8. Example: Here is a table of grades awarded at a university by school.Consider the events:E = grade comes from an Engineering course B = the grade is a B.

  9. Example: Here is a table of grades awarded at a university by school.Consider the events:E = grade comes from an Engineering course B = the grade is a B.

  10. Example: Here is a table of grades awarded at a university by school.Consider the events:E = grade comes from an Engineering course B = the grade is a B.

  11. Note: In conditional probability the condition has the effect of reducing the size of the sample space (i.e. the denominator in the probability fraction)

  12. General Multiplication Rule for Any Two Events:

  13. Example: Slim is still at the poker table. Slim sees 11 cards on the table. Of these, 4 are diamonds. What is the probability of Slim being dealt 2 diamonds from the deck?

  14. If we take the General Multiplication Rule above and divide both sides by P(A) we obtain

  15. Example: Motor vehicles are classified as either light trucks or cars and as either domestic or imported. In early 2004, 69% of vehicles sold were light trucks, 78% were domestic and 55% were domestic light trucks. Let T be the event a vehicle is a light truck and D be the event it is domestic. Write each of the following in terms of events T and D and give the probability.a. The vehicle is a car

  16. Example: Motor vehicles are classified as either light trucks or cars and as either domestic or imported. In early 2004, 69% of vehicles sold were light trucks, 78% were domestic and 55% were domestic light trucks. Let T be the event a vehicle is a light truck and D be the event it is domestic. Write each of the following in terms of events T and D and give the probability.b. The vehicle is an imported car

  17. Example: Motor vehicles are classified as either light trucks or cars and as either domestic or imported. In early 2004, 69% of vehicles sold were light trucks, 78% were domestic and 55% were domestic light trucks. Let T be the event a vehicle is a light truck and D be the event it is domestic. Write each of the following in terms of events T and D and give the probability.c. If a vehicle is a car, what is the probability that it is imported?

  18. Example: Motor vehicles are classified as either light trucks or cars and as either domestic or imported. In early 2004, 69% of vehicles sold were light trucks, 78% were domestic and 55% were domestic light trucks. Let T be the event a vehicle is a light truck and D be the event it is domestic. Write each of the following in terms of events T and D and give the probability.d. Are the events “vehicle is a car” and “vehicle is imported” independent?

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