The contingency table shows how many people wore (Y) and did not wear (N) seat belts as well as how many survived (S) and died (D) in car accidents in a recent year. Wore seat belt Died (D) Total Survived (S) 370,313 Yes (Y) 766 371,079 No (N) 175,079 1314 176,393 Total 545,392 2080 547,472 Complete parts a through d below. a. What is the sample space for a randomly selected individual involved in an auto accident? Use a tree diagram to illustrate the possible outcomes. O A. OB. O C. S D S D S D Sample space: (SS, SD, DS, DD} Y N D S D ... Sample space: (YS, YD, NS, ND} N S S D D Sample space: {YS, YS, ND, ND} O D. N N Y N Sample space: (YY, YN,NY,NN}

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5.

The contingency table provided details the survival (S) and death (D) statistics of individuals who either wore (Y) or did not wear (N) seat belts in a recent year's car accidents.

### Contingency Table:
- **Wore Seat Belt:**
  - **Survived (S):** 370,313
  - **Died (D):** 766
  - **Total:** 371,079

- **Did Not Wear Seat Belt:**
  - **Survived (S):** 175,079
  - **Died (D):** 1,314
  - **Total:** 176,393

- **Overall Totals:**
  - **Survived (S):** 545,392
  - **Died (D):** 2,080
  - **Grand Total:** 547,472

### Question:
What is the sample space for a randomly selected individual involved in an auto accident? Use a tree diagram to illustrate the possible outcomes.

### Options:
- **A:** 
  - Tree Diagram branches into \(S\) and \(D\) for both "Wore Seat Belt" and "Did Not Wear Seat Belt."
  - Sample space: \(\{SS, SD, DS, DD\}\)

- **B:** 
  - Tree Diagram distinguishes “Wore Seat Belt” (Y) and “Did Not Wear Seat Belt” (N), then branches into \(S\) and \(D\).
  - Sample space: \(\{YS, YD, NS, ND\}\)

- **C:** 
  - Similar to option B, but reverses the order of branches. Sample space matches that of B.
  - Sample space: \(\{YS, YS, ND, ND\}\)

- **D:** 
  - Tree diagram branches first by seat belt usage, then aspects unrelated to survival or death.
  - Sample space: \(\{YY, YN, NY, NN\}\) 

This setup helps to visualize how different scenarios might occur based on the use of seat belts and the outcomes of accidents.
Transcribed Image Text:The contingency table provided details the survival (S) and death (D) statistics of individuals who either wore (Y) or did not wear (N) seat belts in a recent year's car accidents. ### Contingency Table: - **Wore Seat Belt:** - **Survived (S):** 370,313 - **Died (D):** 766 - **Total:** 371,079 - **Did Not Wear Seat Belt:** - **Survived (S):** 175,079 - **Died (D):** 1,314 - **Total:** 176,393 - **Overall Totals:** - **Survived (S):** 545,392 - **Died (D):** 2,080 - **Grand Total:** 547,472 ### Question: What is the sample space for a randomly selected individual involved in an auto accident? Use a tree diagram to illustrate the possible outcomes. ### Options: - **A:** - Tree Diagram branches into \(S\) and \(D\) for both "Wore Seat Belt" and "Did Not Wear Seat Belt." - Sample space: \(\{SS, SD, DS, DD\}\) - **B:** - Tree Diagram distinguishes “Wore Seat Belt” (Y) and “Did Not Wear Seat Belt” (N), then branches into \(S\) and \(D\). - Sample space: \(\{YS, YD, NS, ND\}\) - **C:** - Similar to option B, but reverses the order of branches. Sample space matches that of B. - Sample space: \(\{YS, YS, ND, ND\}\) - **D:** - Tree diagram branches first by seat belt usage, then aspects unrelated to survival or death. - Sample space: \(\{YY, YN, NY, NN\}\) This setup helps to visualize how different scenarios might occur based on the use of seat belts and the outcomes of accidents.
Expert Solution
Step 1

Given data indicates how many people wore seat belts (Y) and did not wear seat belts (N) as well as how many survived (S) and died (D) in car accidents.

The objective is to identify the sample space for a randomly selected individual involved in an accident.

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