Conditional Probability

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Presentation transcript:

Conditional Probability

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”

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

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

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) 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 The given condition limits the sample space to non-recycled waste. A favorable outcome is non-recycled plastic. P(plastic | non-recycled) = 20.4 48.9 + 10.1 + 9.1 + 20.4 + 67.8 = 20.4 156.3 0.13 The probability that the non-recycled waste was plastic is about 13%.

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

Conditional Probability – Pets Revisited The table shows the results of a class survey. Find P(own a pet | female) yes no female 8 6 male 5 7 Do you own a pet? 14 females; 12 males Therefore, P(own a pet | female) equals . 4 7

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. Relate: P( male ) = 58% P( male and jogs ) = 20% Define: Let m = male. Let j = jogs. Write: P( j | m ) = P( m and j ) P( m ) = Substitute 0.2 for P(A and B) and 0.58 for P(A). 0.344 Simplify. 0.2 0.58 The probability that a male respondent jogs is about 34%.