A finish inspection at a car manufacturer paint shop assigns one of three scores per car body:

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A finish inspection at a car manufacturer paint shop assigns one of three scores per car body:A perfect with P(A) = 0.85 A-streaks present P(A) = 0.12 A3-air bubbles present with P(A3) = 0.08

A1 means perfect;

A2 only streaks are present;

A3 only air bubbles are present;

A4 streaks and air bubbles are present.

(a) Represent the events A1, A2, A3, and A4 using a Venn diagram.

(b) Calculate the probability for Ai, with i = 1,2,3,4!

(c)Are A and A3 independent events?

(d) What are the sizes of the conditional probabilitiesP(AA3) and P(A3A)?

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