8) The table lists the smoking habits of a group of college students. Sex Non-smoker | Regular Smoker | Heavy Smoker | Total Man 135 182 187 218 322 400 Woman Total 42 21 63 5 10 15 a) If a student is chosen at random, find the probability of getting someone who is a man or a non-smoker. Round your answer to four decimal places. b) If two students are chosen at random without replacement, find the probability of getting both who are heavy smoker and women. Round your answer to four decimal places. c) If a student is chosen at random, find the probability of getting someone who is a woman given she is a regular smoker. Round your answer to four decimal places.

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### Smoking Habits of College Students

The following table displays the smoking habits of a group of college students, categorized by sex and smoking frequency:

| Sex   | Non-smoker | Regular Smoker | Heavy Smoker | Total |
|-------|------------|----------------|--------------|-------|
| Man   | 135        | 42             | 5            | 182   |
| Woman | 187        | 21             | 10           | 218   |
| Total | 322        | 63             | 15           | 400   |

### Probabilities

**a) Probability of Being a Man or a Non-smoker:**
Find the probability that a student chosen at random is either a man or a non-smoker. Provide the answer to four decimal places.

**b) Probability of Two Heavy Smoker Women:**
If two students are chosen at random without replacement, find the probability that both students are heavy smokers and women. Provide the answer to four decimal places.

**c) Probability of a Woman Given She is a Regular Smoker:**
Find the probability that a student is a woman given that she is a regular smoker. Provide the answer to four decimal places.
Transcribed Image Text:### Smoking Habits of College Students The following table displays the smoking habits of a group of college students, categorized by sex and smoking frequency: | Sex | Non-smoker | Regular Smoker | Heavy Smoker | Total | |-------|------------|----------------|--------------|-------| | Man | 135 | 42 | 5 | 182 | | Woman | 187 | 21 | 10 | 218 | | Total | 322 | 63 | 15 | 400 | ### Probabilities **a) Probability of Being a Man or a Non-smoker:** Find the probability that a student chosen at random is either a man or a non-smoker. Provide the answer to four decimal places. **b) Probability of Two Heavy Smoker Women:** If two students are chosen at random without replacement, find the probability that both students are heavy smokers and women. Provide the answer to four decimal places. **c) Probability of a Woman Given She is a Regular Smoker:** Find the probability that a student is a woman given that she is a regular smoker. Provide the answer to four decimal places.
Expert Solution
Step 1

From the provided information,

Sex Non-smoker Regular smoker Heavy smoker Total
Man 135 42 5 182
Woman 187 21 10 218
Total 322 63 15 400
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