Probability of a car having a defect in the brakes or fueling system? Given the following probabilities, defect in brakes = **0.25** defect in transmission = **0.18** defect in fuel = **0.17** defect elsewhere = **0.40** **Q.** What is the probability that the defect is in the brakes or in the fuel system if the probability of both having a brake and fuel defect is 0.15? **Here is my following work/interpretation of the question:** Let B = defective brakes Let F = defective fuel Hence we have the following formula: **Pr(B union F) = Pr(B) + Pr(F) - Pr(B intersection F)** plugging in the numbers and solving the formula we have **Pr(B union F) = 0.25 + 0.17 - 0.15 = 0.27** **Q.** What is the probability of there being no defects in either the brakes or fuel? I believe the answer is: **1-0.27 = 0.73** If I have done something wrong, please if possible explain to me the error that I made. Thank you for looking over my question and have a nice day!

**Ad Q2:**

It is $P(\overline A \cup \overline B)=1-P(A \cap B)$

I replaced F by A.

In a Venn-diagram you can color the events $\overline A$ and $\overline B$. The only remaining uncolored area is the intersection of area F and area B.

First you color the area $\overline A$ blue.

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Then you color the area $\overline B$ yellow. The area, which is now green, is the area, which is colored blue and yellow. The white area hasn´t been colored.

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