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? Not without knowing what the first four cards were

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

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

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

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

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

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. Grade Level SchoolABBelow BTotal Liberal Arts2,1421,8902,2686,300 Engineering ,600 Health Services ,100 Total3,3922,9523,65610,000

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. Grade Level SchoolABBelow BTotal Liberal Arts2,1421,8902,2686,300 Engineering ,600 Health Services ,100 Total3,3922,9523,65610,000

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. Grade Level SchoolABBelow BTotal Liberal Arts2,1421,8902,2686,300 Engineering ,600 Health Services ,100 Total3,3922,9523,65610,000

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)

General Multiplication Rule for Any Two Events:

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?

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

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

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

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?

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?