please show steps and equations used Question 2. (6 Marks] An automobile manufac

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please show steps and equations used

Question 2. (6 Marks] An automobile manufacturer is concerned about a possible recall of its best-selling four-door sedan. If there were a recall, below is a list of the events along with their probability: . a probability of 0.25 of a defect in the brake system . a probability of 0.18 of a defect in the transmission . a probability of 0.21 of a defect in the fuel system a probability of 0.15 of defects in both brake and fuel systems simultaneously, . a probabily of 0.34 of defects in either transmission or fuel system . a probability of 0.1 of defects in transmission and break system, and . a probability of 0.36 of defects in either transmission, asytm or ftel system. Suppose there is a recall, determine the probability that a) [2 marks] the defects are in break and fuel systems and transmission b) 12 marks] there is only one defect. c) 12 marks] the defect is in other systems (not in the break, fuel nor transmission system.

Explanation / Answer

Let Brake Transmission and Fuel be denoted by B, T and F respectively

P(B) = 0.25

P(T) = 0.18

P(F) = 0.21

P(B and F) = 0.15

P(T or F) = 0.34

P(T and B) = 0.11

P(T or B or F) = 0.36

P(T and F) = P(T) + P(F) - P(T or F)

P(T and F) = 0.18 + 0.21 - 0.34 = 0.05

a) P(B and F and T) = ?

P(B or F or T) = P(B) + P(F) + P(T) - P(B and F) - P(F and T) - P(B and T) + P(B and F and T)

0.36 = 0.25 + 0.18 + 0.21 - 0.15 - 0.11 - 0.05 + P(B and F and T)

P(B and F and T) = 0.03

b)  P(B only) + P(F only) + P(T only) =?

P(B only) + P(F only) + P(T only) = P(B or F or T)  - P(B and F) - P(F and T) - P(B and T) + 2*P(B and F and T)

P(B only) + P(F only) + P(T only) = 0.36  - 0.15 - 0.11 - 0.05 + 0.06

P(B only) + P(F only) + P(T only) = 0.11

c) P(defect in other) = 1- P(B or F or T)  

P(defect in other) = 1- 0.36

P(defect in other) = 0.64

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