The three most popular options on a certain type of newcar are a built-in GPS (A), a sunroof (B), and an automatictransmission (C). If 40% of all purchasers requestA, 55% request B, 70% request C, 63% request A or B,77% request A or C, 80% request B or C, and 85%request A or B or C, determine the probabilities of thefollowing events. [Hint: “A or B” is the event that at leastone of the two options is requested; try drawing a Venndiagram and labeling all regions.]a. The next purchaser will request at least one of thethree options.b. The next purchaser will select none of the three options. c. The next purchaser will request only an automatictransmission and not either of the other two options.d. The next purchaser will select exactly one of thesethree options.
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 40% of all purchasers request
A, 55% request B, 70% request C, 63% request A or B,
77% request A or C, 80% request B or C, and 85%
request A or B or C, determine the probabilities of the
following events. [Hint: “A or B” is the
one of the two options is requested; try drawing a Venn
diagram and labeling all regions.]
a. The next purchaser will request at least one of the
three options.
b. The next purchaser will select none of the three options.
c. The next purchaser will request only an automatic
transmission and not either of the other two options.
d. The next purchaser will select exactly one of these
three options.
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