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.

(a) Are being in excellent health and having health coverage mutually exclusive?

(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) Do having excellent health and having health coverage appear to be independent?

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Health No Coverage Yes Total Excellent 0.0230 0.2099 0.2329 Health Status Good Fair Poor Total 0.0427 0.0192 0.0050 0.1262 0.2410 0.0817 0.0289 0.8738 0.2838 0.1009 0.0338 1.0000 Very good 0.0364 0.3123 0.3486