1. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 12.7 Conditional Probability

2. Copyright 2013, 2010, 2007, Pearson, Education, Inc. What You Will Learn Conditional Probability 12.7-2

3. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Conditional Probability In general, the probability of event E 2 occurring, given that an event E 1 has happened (or will happen; the time relationship does not matter), is called a conditional probability and is written P(E 2 |E 1 ). 12.7-3

4. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 1: Using Conditional Probability A single card is selected from a deck of cards. Determine the probability it is a club, given that it is black. 12.7-4

5. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 1: Using Conditional Probability Solution The card is black, so only 26 cards are possible, 13 of which are clubs. 12.7-5

6. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Conditional Probability For any two events E 1 and E 2, the conditional probability, P(E 2 |E 1 ), is determined as follows. 12.7-6

7. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 3: Using the Conditional Probability Formula Two hundred and fifty patients who had knee, hip, or heart surgery were asked whether they were satisfied, dissatisfied, or neutral regarding the results of their surgery. The responses are given in the table on the next slide. 12.7-7

8. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 3: Using the Conditional Probability Formula If one person from the 250 patients surveyed is selected at random, determine the probability that the person 12.7-8

9. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 3: Using the Conditional Probability Formula a) was satisfied with the results of the surgery. Solution 12.7-9

10. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 3: Using the Conditional Probability Formula b) was satisfied with the results of the surgery, given that the person had knee surgery. Solution 12.7- 10

11. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 3: Using the Conditional Probability Formula c) was dissatisfied with the results of the surgery, given that the person had hip surgery. Solution 12.7- 11

12. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 3: Using the Conditional Probability Formula d) had heart surgery, given that the person was dissatisfied with the results of the surgery. Solution 12.7- 12