Question: In joint probability tables knowing only a few probabilities will

In joint probability tables, knowing only a few probabilities will often allow the user to fll in the entire table with minimal effort. The table below shows partial results from a survey of 200 cattle ranchers and dairy farmers. The survey asked, “How concerned are you about the spread of Mad Cow Disease to your herd?” With the information provided, fll in the joint probability table below (including the marginal values) and use the table to answer the questions that follow.
a. What percent of the dairy farmers are “very concerned”?
b. What percent of the “very concerned” responses came from dairy farmers?
c. If you choose someone randomly from the study and learn that he/she responded “unconcerned” to the survey question, how likely is it that the response came from a cattle rancher?
d. Are level of concern and type of business statistically independent?

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