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Section 3.2

Section 3.2. Conditional Probability. Independent or Dependent Events. Two events A and B are independent if event B is not affected by the occurrence of event A. A = 1st child is a boy B = 2nd child is a boy. A = Being female B = Having brown hair.

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Section 3.2

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  1. Section 3.2 Conditional Probability

  2. Independent or Dependent Events Two events A and B are independentif event B is not affected by the occurrence of event A. A = 1st child is a boy B = 2nd child is a boy A = Being female B = Having brown hair When event A affects event B, they are dependent. A = taking an aspirin each day B = having a heart attack A = studying for a test B = making an A on a test

  3. With replacement = independent What is the probability of drawing three kings with replacement? With or Without Replacement • Without replacement = dependent • What is the probability of drawing three kings without replacement?

  4. Practicing the piano, and then becoming a concert pianist. Tossing a coin, getting a head, then rolling a die and getting a 6. Selecting a king from a standard deck, replacing it, and then selecting a queen from the deck. Selecting a king from a standard deck, not replacing it, and then selecting a queen from the deck. Parking beside a fire hydrant on Tuesday and getting a parking ticket on Tuesday. A numbered ball between 1 and 40 is selected from a bin, and then a second numbered ball is selected from the remaining balls in the bin. Independent or Dependent?

  5. Conditional probability: Event B is dependent on event A. P(B│A) (read B│A as “B given A.”) Notation for Conditional Probability

  6. Contingency Table The results of responses when a sample of adults in 3 cities was asked if they liked a new juice is: Omaha Seattle Miami Total Yes 100 150 150 400 No 125 130 95 350 Undecided 75 170 5 250 Total 300 450 250 1000 One of the responses is selected at random. Find: 1. P(Yes) 2. P(Seattle) 3. P(Miami) 4. P (No │given Miami) 1. P (No │given Omaha) 2. P (yes │given Omaha) 3. P (Miami │given No) 4. P (yes │given Seattle)

  7. Class practice

  8. Worksheet 3-2 Conditional Probability HW, finish Chapter 1 and 2 Review, Accelerated Math Quiz tomorrow on Basic Probability (3-1) Homework

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