The three most popular options on a certain type of new car are a built-in GPS (

Question

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 20% of purchasers request A, 40% request B, 65% request C, 53% request A or B, 77% request A or C, 85% request B or C, and 5% request A and B and C, determine the probabilities of the following events. [Hint: “A or B” is the event that at least one of the two options are purchased; try drawing a Venn diagram and labeling all regions.]

A. The next purchaser will NOT request A. (2pts)

B. The next purchaser will request at least one of the three options. (2pts)

C. The next purchaser will select none of the three options. (3pts)

D. The next purchaser will request only C and not either of the other two options. (3pts)

Explanation / Answer

as P(A n B) =P(A)+P(B)-P(A U B)

a) P(next purchaser will NOT request A)=1-0.20=0.80

b)P(next purchaser will request at least one of the three options)

c)

purchaser will select none of the three options =1-P(A U B UC) =1-0.95 =0.05

d)next purchaser will request only C and not either of the other two options

=P(C)-P(A n C)-P(B n C)+P(A n B nC)=0.65-0.08-0.2+0.05=0.42

P(A)= 0.2 P(B)= 0.4 P(C)= 0.65 P(AnB)= 0.07 P(BnC)= 0.2 P(AnC)= 0.08 P(AUB)= 0.53 P(BUC)= 0.85 P(AUC)= 0.77 P(AnBnC) = 0.05

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