(Solved): The three most popular options on a certain type of new car are a built-in GP ...

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The three most popular options on a certain type of new car are a built-in GPS $$(A)$$, a sunroof $$(B)$$, and an automatic transmission (C). If $$49\%$$ of all purchasers request $$A,56\%$$ request $$B,80\%$$ request $$C,64\%$$ request $$A$$ or $$B,87\%$$ request $$A$$ or $$C,91\%$$ request $$B$$ or $$C$$, and $$95\%$$ request $$A$$ or $$B$$ or $$C$$, determine the probabilities of the following events. [Hint: "A or $$B$$ " is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] (Round your answers to 2 decimal places, if needed.) (a) The next randomly selected purchaser will request at least one of the three options. (b) The next randomly selected purchaser will select none of the three options. (c) The next randomly selected purchaser will request only an automatic transmission and not either of the other two options. (d) The next randomly selected purchaser will select exactly one of these three options.