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Essential Question: What makes conditional probability different from normal probability?

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A conditional probability contains a condition that may limit the sample space for the event. We can write a conditional probability event using the notation P(B | A), which means “the probability of event B, given event A”. Order matters when calculating conditional probability. We can calculate conditional probability from a table (next slide)

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The table below shows the results of a class survey if students did a household chore last night. Find P(did a chore | male) The second condition limits the sample space to only males (15 total). Of those 15, 7 did a chore, so P(did a chore | male) = 7 / 15 Use the table above to find P(female | did a chore) YesNo Male78 Female76 7 / 14 = 1 / 2

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Y OUR T URN The table below shows recycling data for a recent year. Find the probability that a sample of recycled waste was paper. Find P(paper | recycled) 36.7 / 68 .54 MaterialRecycledNot Recycled Paper36.745.1 Metal6.311.9 Glass2.410.1 Plastic1.424.0 Other21.270.1

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You can use a formula to find conditional probability P(B | A) = P(A and B) P(A) Example: 80% of an airline’s flights depart on schedule. 72% of its flights depart and arrive on schedule. Find the probability that a flight that departs on time also arrives on time. .72 /.80 = 0.9

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Y OUR T URN P(B | A) = P(A and B) P(A) Researchers asked people who exercise regularly whether they jog or walk. 58% of the respondents were male. 20% of all respondents were males who said they jog. Find the probability that a male respondent jogs. .20 /.58 = 0.34 (about 34%)

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You can use a tree diagram to solve problems involving conditional probabilities. A student in Buffalo, NY made the following observations: Of all snowfalls, 5% are heavy (at least 6 in) After a heavy snowfall, schools are closed 67% of the time After a light (less than 6 in) snowfall, schools are closed 3% of the time. Find the probability that the snowfall is light and the schools are open (next slide)

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5% are heavy snowfall After heavy, 67% chance school closed After light, 3% chance school closed Find P(light snow and schools open) 0.05 0.95 Heavy Light 0.67 0.33 0.03 0.97 Closed Open Closed Open 0.95 0.97 = 0.92

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Y OUR T URN Find P(schools open and heavy snow) 0.05 0.95 Heavy Light 0.67 0.33 0.03 0.97 Closed Open Closed Open 0.05 0.33 = 0.0165

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A SSIGNMENT Page 656 – 657 Problems 1 – 12 (all)

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