11 4 CONDITIONAL PROBABILITY Learning Goal find conditional

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? YES NO MALE 7 8 FEMALE 7 6 What type of college do you attend? MALE FEMALE 2462 2 YR COLLEGE 1866 5517 4 YR COLLEGE 4324 1954 GRADUATE SCHOOL 1349 Find P(did a chore│male) 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)