A survey of 200 cell phone users in metro Detroit asked, among other things, the county they reside in and their cell phone service provider. The data are summarized in the contingency table shown below. What is the probability a randomly selected survey respondent who lives in Wayne county has Verizon, i.e., find P(V | W). Cell Phone Service Provider County Macomb (M) Oakland (0) Sprint (S) AT&T (A) Verizon (V) Row Total 17 25 50 19 38 13 70 Wayne (W) Col Total 24 37 19 80 60 100 40 200

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A survey of 200 cell phone users in metro Detroit asked, among other things, the county they reside in and their cell phone service provider. The data are summarized in the contingency table shown below. What is the probability a randomly selected survey respondent who lives in Wayne county has Verizon, i.e., find P(V | W).

### Cell Phone Service Provider

| County   | Sprint (S) | AT&T (A) | Verizon (V) | Row Total |
|----------|------------|----------|-------------|-----------|
| Macomb (M)  | 17         | 25       | 8           | 50        |
| Oakland (O) | 19         | 38       | 13          | 70        |
| Wayne (W)   | 24         | 37       | 19          | 80        |
| **Col Total** | **60**      | **100**    | **40**        | **200**     |

**Explanation:**
This table depicts the distribution of cell phone service providers among respondents from three counties: Macomb, Oakland, and Wayne. Each cell in the table indicates the number of survey respondents from a specific county using a particular service provider. For instance, in Wayne County, out of 80 respondents, 24 use Sprint, 37 use AT&T, and 19 use Verizon. The column and row totals represent the sum of respondents for each provider and county, respectively. 

The probability that a randomly selected respondent from Wayne County uses Verizon is calculated as follows:

\[ P(V | W) = \frac{\text{Number of Verizon users in Wayne}}{\text{Total number of respondents in Wayne}} = \frac{19}{80} \approx 0.2375 \]

This indicates that approximately 23.75% of respondents from Wayne County use Verizon.
Transcribed Image Text:A survey of 200 cell phone users in metro Detroit asked, among other things, the county they reside in and their cell phone service provider. The data are summarized in the contingency table shown below. What is the probability a randomly selected survey respondent who lives in Wayne county has Verizon, i.e., find P(V | W). ### Cell Phone Service Provider | County | Sprint (S) | AT&T (A) | Verizon (V) | Row Total | |----------|------------|----------|-------------|-----------| | Macomb (M) | 17 | 25 | 8 | 50 | | Oakland (O) | 19 | 38 | 13 | 70 | | Wayne (W) | 24 | 37 | 19 | 80 | | **Col Total** | **60** | **100** | **40** | **200** | **Explanation:** This table depicts the distribution of cell phone service providers among respondents from three counties: Macomb, Oakland, and Wayne. Each cell in the table indicates the number of survey respondents from a specific county using a particular service provider. For instance, in Wayne County, out of 80 respondents, 24 use Sprint, 37 use AT&T, and 19 use Verizon. The column and row totals represent the sum of respondents for each provider and county, respectively. The probability that a randomly selected respondent from Wayne County uses Verizon is calculated as follows: \[ P(V | W) = \frac{\text{Number of Verizon users in Wayne}}{\text{Total number of respondents in Wayne}} = \frac{19}{80} \approx 0.2375 \] This indicates that approximately 23.75% of respondents from Wayne County use Verizon.
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