(Ch5) Use the following contingency table to find the conditional probability that a r did not smoked during pregnancy given that she had some college experience but r college degree. Mother's Education Below High School High School Some College College Degree Column Total Select one: a. 0.2736 O b. 0.8752 O C. O d. 0.9197 0.8399 Smoked during Didn't Smoke Pregnancy 393 560 121 48 1,122 during Pregnancy 640 1,384 635 550 3.209 Row Total 1,033 1,944 756 598 4,331
(Ch5) Use the following contingency table to find the conditional probability that a r did not smoked during pregnancy given that she had some college experience but r college degree. Mother's Education Below High School High School Some College College Degree Column Total Select one: a. 0.2736 O b. 0.8752 O C. O d. 0.9197 0.8399 Smoked during Didn't Smoke Pregnancy 393 560 121 48 1,122 during Pregnancy 640 1,384 635 550 3.209 Row Total 1,033 1,944 756 598 4,331
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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![**Conditional Probability and Contingency Table Analysis**
*(Ch5) Use the following contingency table to find the conditional probability that a mother did not smoke during pregnancy, given that she had some college experience but no college degree.*
| Mother’s Education | Smoked during Pregnancy | Didn’t Smoke during Pregnancy | Row Total |
|--------------------------|-------------------------|-------------------------------|-----------|
| Below High School | 393 | 640 | 1,033 |
| High School | 560 | 1,384 | 1,944 |
| Some College | 121 | 635 | 756 |
| College Degree | 48 | 550 | 598 |
| **Column Total** | **1,122** | **3,209** | **4,331** |
Select one:
- a. 0.2736
- b. 0.8752
- c. 0.8399
- d. 0.9197
**Solution Explanation:**
To find the conditional probability that a mother did not smoke during pregnancy given that she had some college experience, use the formula for conditional probability:
\[
P(\text{Didn’t Smoke | Some College}) = \frac{\text{Number of mothers with some college who didn't smoke}}{\text{Total number of mothers with some college}}
\]
Based on the table:
- Number of mothers with some college who didn’t smoke = 635
- Total number of mothers with some college = 756
Calculate:
\[
P(\text{Didn’t Smoke | Some College}) = \frac{635}{756} \approx 0.8399
\]
The correct answer is **c. 0.8399**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5c9e71a-2152-46c3-8ddc-78ecbd167355%2F8c3d7617-6359-4707-861d-6028ad573ec8%2Fjefglun_processed.png&w=3840&q=75)
Transcribed Image Text:**Conditional Probability and Contingency Table Analysis**
*(Ch5) Use the following contingency table to find the conditional probability that a mother did not smoke during pregnancy, given that she had some college experience but no college degree.*
| Mother’s Education | Smoked during Pregnancy | Didn’t Smoke during Pregnancy | Row Total |
|--------------------------|-------------------------|-------------------------------|-----------|
| Below High School | 393 | 640 | 1,033 |
| High School | 560 | 1,384 | 1,944 |
| Some College | 121 | 635 | 756 |
| College Degree | 48 | 550 | 598 |
| **Column Total** | **1,122** | **3,209** | **4,331** |
Select one:
- a. 0.2736
- b. 0.8752
- c. 0.8399
- d. 0.9197
**Solution Explanation:**
To find the conditional probability that a mother did not smoke during pregnancy given that she had some college experience, use the formula for conditional probability:
\[
P(\text{Didn’t Smoke | Some College}) = \frac{\text{Number of mothers with some college who didn't smoke}}{\text{Total number of mothers with some college}}
\]
Based on the table:
- Number of mothers with some college who didn’t smoke = 635
- Total number of mothers with some college = 756
Calculate:
\[
P(\text{Didn’t Smoke | Some College}) = \frac{635}{756} \approx 0.8399
\]
The correct answer is **c. 0.8399**.
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