Page of 53 2OOM 25. The three major options on a certain type of new car are an

Question

Page of 53 2OOM 25. The three major options on a certain type of new car are an automatic transmission (A), a sunroof (B), and a stereo with CD player (C). If 70% of all purchasers request A, 80% request B, 75% request C, 85% request A or B, 90% request A or C, 95% request B or C, and 98% request A or B or C, compare the probabilities of the following events. 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.

Explanation / Answer

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

and

therefore from above"

a)

b)

P(none ) =1- P(AUBUC) =1-0.98 =0.02

c)

probability =P(A) -P(AnB)-P(AnC) +P(AnBnC) =0.7-0.65-0.55+0.53 =0.03

d)

all =P(AnBnC)= P(A)+P(B)+P(C )-P(AnB)-P(BnC)-P(AnC)+P(AnBnC) =0.53

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