Question 15

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 37% of all purchasers request A, 48% request B, 65% request C, 58% request A or B, 74% request A or C, 73% request B or C, and 80% 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.]

Events:

  • - A purchaser requests a built-in GPS.
  • - A purchaser requests a sunroof.
  • - A purchaser requests an automatic transmission.

Probabilities:

  • .
  • .
  • .
  • .
  • .
  • .
  • .

(a)

Problem: The next purchaser will request at least one of the three options.

Process: ...

Answer: 0.8.

(b)

Problem: The next purchaser will select none of the three options.

Process: ...

Answer: 0.2.

(c)

Problem: The next purchaser will request only an automatic transmission and not either of the other two options.

Process: ...

Answer: 0.22.

(d)

Problem: The next purchaser will select exactly one of these three options.

Process: ...

Answer: 0.35.