(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.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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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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