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Unit: Probability 12-2: Conditional Probability

Essential Question: What makes conditional probability different from normal probability?. Unit: Probability 12-2: Conditional Probability.

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Unit: Probability 12-2: Conditional Probability

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  1. Essential Question: What makes conditional probability different from normal probability? Unit: Probability12-2: Conditional Probability

  2. 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) 12-2: Conditional Probability

  3. 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) 12-2: Conditional Probability 7/14 = 1/2

  4. Your Turn • 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) 12-2: Conditional Probability 36.7/68 .54

  5. 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. 12-2: Conditional Probability .72/.80 = 0.9

  6. Your Turn • 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. 12-2: Conditional Probability .20/.58 = 0.34 (about 34%)

  7. 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) 12-2: Conditional Probability

  8. 5% are heavy snowfall After heavy, 67% chance school closed After light, 3% chance school closed Find P(light snow and schools open) 12-2: Conditional Probability Closed 0.67 Heavy Open 0.05 0.33 0.95  0.97 = 0.92 Closed 0.03 Light 0.95 0.97 Open

  9. Your Turn • Find P(schools open and heavy snow) 12-2: Conditional Probability Closed 0.67 Heavy Open 0.05 0.33 0.05  0.33 = 0.0165 Closed 0.03 Light 0.95 0.97 Open

  10. Assignment • Page 656 – 657 • Problems 1 – 12 (all) 12-2: Conditional Probability

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