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In-s [12.5K]
3 years ago
6

What statements apply?

Mathematics
1 answer:
IgorLugansk [536]3 years ago
6 0

Life

Hope this helps! ^-^

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Complete question is;

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.

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(b) What is the probability that there are no defects in either the brakes or the fueling system?

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A) 0.27

B) 0.73

Step-by-step explanation:

Let B denote that there is a defect in the break system

Let T demote that there is a defect in transmission

Let F denote that there is a defect in the fuel system.

Let P denote that there is a defect in some other area.

Now, we are given;

P(B) = 0.25

P(T) = 0.18

P(F) = 0.17

P(O) = 0.40

A) We are given that probability of defects in both brakes and the fueling system simultaneously is 0.15.

Thus, it means; P(B ⋂ F) = 0.15

Now, we want to find the probability that the defect is the brakes or the fueling system. This is expressed as;

P(B ⋃ F) = P(B) + P(F) - P(B ⋂ F)

Plugging in the relevant values to give;

P(B ⋃ F) = 0.25 + 0.17 - 0.15

P(B ⋃ F) = 0.27

B) We want to find the probability that there are no defects in either the brakes or the fueling system.

This is expressed as;

P(B' ⋃ F') = 1 - P(B ⋃ F)

Plugging in relevant value;

P(B' ⋃ F') = 1 - 0.27

P(B' ⋃ F') = 0.73

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