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Question 1135873: 2.18 Health coverage, relative frequencies: 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) conditional on whether or not they have health insurance.
(please round any numerical answers to 4 decimal places)
Excellent Very Good Good Fair Poor Total
No Coverage 0.023 0.0364 0.0427 0.0192 0.005 0.1262
Coverage 0.2099 0.3123 0.241 0.0817 0.0289 0.8738
Are being in excellent health and having health coverage mutually exclusive?
not mutually exclusive
mutually exclusive
Explain your reasoning:
b) What is the probability that a randomly chosen individual has excellent health?
c) What is the probability that a randomly chosen individual has excellent health given that he has health coverage?
d) What is the probability that a randomly chosen individual has excellent health given that he doesn't have health coverage?
e) Does having excellent health and having health coverage appear to be independent?
being in excellent health and having health coverage are independent
being in excellent health and having health coverage are dependent
Explain your reasoning:
Here's a screenshot of the problem: https://prnt.sc/msbe5g
Thank you!
Answer by VFBundy(438)   (Show Source):
You can put this solution on YOUR website! Are being in excellent health and having health coverage mutually exclusive?
No. It is possible to be in excellent health without having health coverage. It is also possible to have health coverage without being in excellent health.
b) What is the probability that a randomly chosen individual has excellent health?
0.2329
c) What is the probability that a randomly chosen individual has excellent health given that he has health coverage?
0.2099/0.8738 = 0.2402
d) What is the probability that a randomly chosen individual has excellent health given that he doesn't have health coverage?
0.023/0.1262 = 0.1823
e) Does having excellent health and having health coverage appear to be independent?
No. A randomly chosen person who has health coverage is 24.02% likely to be in excellent health, whereas a randomly chosen person who does not have health coverage is only 18.23% likely to be in excellent health. That means a person who does not have health coverage is only 0.1823/0.2402...or 0.7590 (75.90%)...as likely to be in excellent health than a person who has health coverage.
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