(a) Why is being in excellent health and having health coverage not mutally exclusive? Please leave a detailed answer and how you found out. (b) If we draw one individual at random, what is the probability that the respondent has excellent health or doesn't have health coverage? Please leave a detailed answer on how you found that answer. (c) What is the probability that a randomly chosen individual has excellent health given that he has health coverage? Please show all work needed to answer this question. Please be very detailed on how you got the answer. (d) What is the probability that a randomly chosen individual has excellent health given that he doesn't have health coverage? please be very detailed on how you got the answer.
The Behavioral Risk Factor Surveillance System (BRFSS) is an annual telephone survey designed to identify risk factors in the adult population and report emerging health trends. The following table displays the distribution of health status of respondents to this survey (excellent, very good, good, fair, poor) and whether or not they have health insurance.
| Excellent | Very good | Good | Fair | Poor | Total | |
|---|---|---|---|---|---|---|
| No health coverage | 459 | 727 | 854 | 385 | 99 | 2524 |
| Health coverage | 4198 | 6245 | 4821 | 1634 | 578 | 17476 |
| Total | 4657 | 6972 | 5675 | 2019 | 667 | 20000 |
(a) Why is being in excellent health and having health coverage not mutally exclusive? Please leave a detailed answer and how you found out.
(b) If we draw one individual at random, what is the probability that the respondent has excellent health or doesn't have health coverage? Please leave a detailed answer on how you found that answer.
(c) What is the probability that a randomly chosen individual has excellent health given that he has health coverage? Please show all work needed to answer this question. Please be very detailed on how you got the answer.
(d) What is the probability that a randomly chosen individual has excellent health given that he doesn't have health coverage? please be very detailed on how you got the answer.
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