2. (15 pts) The three maior options on a certain type of new car are an automati

Question

2. (15 pts) The three maior options on a certain type of new car are an automatic transmission (A), a sunroof (B), and a stereo with CD player (C). If 86% of all purchasers request A, 70% request B. 64% request C, 91 % request A or request A or C. 80 % request B or C, and 96% request A or B or Compare the probabilities of the following events. a. (3) The next purchaser will request b. (4) The next purchas c. (4) The next purchase B, 94% C. at least one of the three options. er will select none of the three options. r will request only a CD player and not either of the other two options. (4) The next t purchaser will select exactly one of the three options.

Explanation / Answer

1) The next purchaser will request at least one of the three options is people should request either A or B or C

is 96 %

Propability of the next purchaser will request at least one of the three options = 96/100

= 0.96

2)Probability of the next purchaser will request at none of the three options = 1- Probability of the next purchaser will request at least one of the three options

= 1 - 0.96

= 0.04

3) Probability of the next purchaser will request only CD player = Probability of the next purchaser will request at least one of the three options - Probability of the next purchaser will request either automatic transmission or sunroof

= 0.96 - 0.91

= 0.05

4) Probability the next purchaser will select one of the three options = Probability of the next purchaser will request only CD player + Probability of the next purchaser will request only automatic transmission + Probability of the next purchaser will request only sunroof

= ( 0.96 - 0.91) + (0.96 - 0.8) + (0.96 - 0.94)

= 0.05 + 0.16 + 0.02

= 0.23

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