A contain sports car comes equipped with either an automatic or a manual transmi

Question

A contain sports car comes equipped with either an automatic or a manual transmission, and the car is available in one of four colors. Relevant probabilities for various combinations of transmission type and color are given in the accompanying table. Let A = (automatic transmission), B = {black}, and C = {white}. Calculate P(A) and P(A intersection B) Calculate both P(A|B) and P(B|A). An automobile service facility specializing in engine tune-ups knows that 50% of all tune-ups are done on four-cylinder automobiles, 40% on cylinders automobiles, and 10% on eight-cylinder automobiles. Let X = the number of cylinders on the next car to be tuned.

Explanation / Answer

Solution: Please see the solution of question 1 with two subparts (a) and (b)

(1.a)

P(A) = (0.13 + 0.10 + 0.11 + 0.11) = 0.45

P(A B) = 0.11

(1. b)

P(B) = 0.11 + 0.15 = 0.26

P(A | B) = P(A B) / P(B)

             = 0.11 / 0.26

             = 0.42

P(B | A) = P(A B) / P(A)

             = 0.11 / 0.45

             = 0.24

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.