11.4 CONDITIONAL PROBABILITY Learning Goal find conditional probabilities use table and tree diagrams to determine conditional probabilities

A conditional probability contains a condition that may limit the sample space for an event. The probability that an event b will occur given that another event, a, has already occurred The two events must be dependent

FIND THE CONDITIONAL PROBABILITY Did you do a chore last night? YESNO MALE78 FEMALE76 Find P(did a chore │ male) What type of college do you attend? MALEFEMALE 2 YR COLLEGE YR COLLEGE GRADUATE SCHOOL Find P(female │ grad school) Find P(female │ did a chore) Find P(4 year │ male)

Eighty percent of an airline’s flights depart on schedule. Seventy-two percent of its flights depart and arrive on schedule. Find the probability that a flight that departs on times also arrives on time. Researchers asked people who exercise regularly whether they jog or walk. Fifty-eight percent of the respondents were male. Twenty percent of all respondents were male who said that they jog. Find the probability that a male respondent jogs.

MAKE A TREE DIAGRAM WITH THE GIVEN INFORMATION Of all snowfalls, 5% are heavy After a heavy snowfall, schools are closed 67% of the time After a light snowfall, schools are closed 3% of the time Find the probability that the snowfall is light and the schools are closed. Find p(schools open, given heavy snow)

MAKE A TREE DIAGRAM WITH THE GIVEN INFORMATION A school system compiled the following information from a survey it sent to people who were juniors 10 years earlier. 85% of the students graduated from high school Of the students who graduated, 90% are happy with their present job Of the students who did not graduate, 60% are happy with their present job Find the probability that the person graduated and is happy. Find p(did not graduate and is happy)