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Warm-up

Warm-up . The following table shows the number of people that like a particular fast food restaurant. Is the probability of liking McDonald’s dependent on the gender of the person surveyed? Explain using calculations. What about Burger King and Wendy’s?. Warm-up .

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Warm-up

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  1. Warm-up • The following table shows the number of people that like a particular fast food restaurant. • Is the probability of liking McDonald’s dependent on the gender of the person surveyed? Explain using calculations. • What about Burger King and Wendy’s?

  2. Warm-up • Howard is playing a carnival game. The object of the game is to predict the sum you will get by spinning spinner A and then spinner B. Howard predicts he will get a sum of 5. • List the sample space. • What is the probability Howard gets a sum of 5? • Suppose that Howard gets a 3 on Spinner A, what is the new probability of him getting a sum of 5? 3/12 or 1/4 1/3

  3. Conditional Probability

  4. Conditional Probability • Conditional Probability contains a condition that may limit the sample space for an event. • You can write a conditional probability using the notation - This reads “the probability of event B, given event A”

  5. yes no female 8 6 male 5 7 Do you own a pet? 8 14 Therefore, P(own a pet | female) equals . Conditional Probability The table shows the results of a class survey. Find P(own a pet | female) 14 females; 12 males The condition female limits the sample space to 14 possible outcomes. Of the 14 females, 8 own a pet.

  6. yes no female 7 6 male 7 8 Did you wash the dishes last night? 7 15 Therefore, P(wash the dishes | male) Conditional Probability The table shows the results of a class survey. Find P(wash the dishes | male) 13 females; 15 males The condition male limits the sample space to 15 possible outcomes. Of the 15 males, 7 did the dishes.

  7. Material Recycled Not Recycled Paper 34.9 48.9 Metal 6.5 10.1 Glass 2.9 9.1 Plastic 1.1 20.4 Other 15.3 67.8 20.4 48.9 + 10.1 + 9.1 + 20.4 + 67.8 P(plastic | non-recycled) = 20.4 156.3 = 0.13 Let’s Try One Using the data in the table, find the probability that a sample of not recycled waste was plastic. P(plastic | non-recycled) The given condition limits the sample space to non-recycled waste. A favorable outcome is non-recycled plastic. The probability that the non-recycled waste was plastic is about 13%.

  8. Conditional Probability Formula • For any two events A and B from a sample space with P(A) does not equal zero

  9. Relate: P( male ) = 58% P( male and jogs ) = 20% Define: Let m = male. Let j = jogs. P( m and j ) P( j ) Write: P( j | m ) = 0.2 0.58 = Substitute 0.2 for P(A and B) and 0.58 for P(A). 0.344 Simplify. Conditional Probability 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 males who said they jog. Find the probability that a person randomly selected jogs given they are male. The probability that a male respondent jogs is about 34%.

  10. yes no female 8 6 male 5 7 Do you own a pet? 4 7 Therefore, P(own a pet | female) equals . Conditional Probability – Pets Revisited The table shows the results of a class survey. Find P(own a pet | female) 14 females; 13 males

  11. Homework • Practice Worksheet

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