An automobile manufacturer is concerned about a possible recall of its best-selling four-door sedan. If there were a recall, there is a probability of 0.25 of a defect in the brake system, 0.18 of a defect in the transmission, 0.17 of a defect in the fuel system, and 0.40 of a defect in some other area. (a) What is the probability that the defect is the brakes or the fueling system if the probability of defects in both systems simultaneously is 0.15?

Question

Jimena Higgins

Mathematics

25 September, 02:10

An automobile manufacturer is concerned about a possible recall of its best-selling four-door sedan. If there were a recall, there is a probability of 0.25 of a defect in the brake system, 0.18 of a defect in the transmission, 0.17 of a defect in the fuel system, and 0.40 of a defect in some other area. (a) What is the probability that the defect is the brakes or the fueling system if the probability of defects in both systems simultaneously is 0.15?

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Connor Clark · Answer 1

0.27

Step-by-step explanation:

Suppose A is the event of defect in the brake system and B is the event of defect in the fuel system,

We have given,

P (A) = 0.25,

P (B) = 0.17

P (A∩B) = 0.15 (the probability of defects in both systems simultaneously is 0.15),

We know that,

P (A∪B) = P (A) + P (B) - P (A∩B)

= 0.25 + 0.17 - 0.15

= 0.27

Hence, the probability that the defect is the brakes or the fueling system is 0.27.