copyright 2013, 2010, 2007, pearson, education, inc. section 12.7 conditional probability

Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section 12.7

Conditional Probability


What You Will Learn


12.7-2



In general, the probability of

event E2 occurring, given that an

event E1 has happened (or will

happen; the time relationship does not matter), is called a conditional probability and is

written P(E2|E1).12.7-3


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.

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Example 1: Using Conditional Probability

SolutionThe card is black, so only 26 cards are possible, 13 of which are clubs.

P(club|black) or P(C | B)

13

26

1

2

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For any two events E1 and E2, the

conditional probability, P(E2|

E1), is determined as follows.

P E2| E

1 n E1 and E

2 n E

1 12.7-6


Example 3: Using the Conditional Probability FormulaTwo 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


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

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a) was satisfied with the results of the surgery.Solution

P(satisfied)

205

250

41

5012.7-9



b) was satisfied with the results of the surgery, given that the person had knee surgery.Solution

P sat | knee n both n knee

70

95

14

1912.7-10



c) was dissatisfied with the results of the surgery, given that the person had hip surgery.Solution

P dissat | hip n both n hip

15

105

1

712.7-11



d) had heart surgery, given that the person was dissatisfied with the results of the surgery.Solution

P heart | dissat n both n dissat

5

45

1

912.7-12

copyright 2013, 2010, 2007, pearson, education, inc. section 12.7 conditional probability

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