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

Question

A certain 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 = {blue}, C = {white}, R = {Red}, and M = {manual transmission}. a. Calculate the probability of having an automatic transmission or a blue car. b. If the selected car has an manual transmission, what is the probability that the color of the car is red?

Explanation / Answer

The Table can be rewritten as below. The probability of having a white colour automatic transmission car

= 1 - (0.13 + 0.10 + 0.11 +0.11 + 0.07 +0.15 + 0.18) = 1-0.85 = 0.15

(a) P(Automatic Transmission or a Blue Car) = P(A) + P(B) - P(A and B)(since this has been taken into account in P(A))

P (A or B) = 0.45 + 0.17 - 0.10 = 0.52

(b) The question is find P(R), given that the car has a manual Transmission i.e P(R/M)

By Bayes Theorem P(R/M) = P ( R and M) / P(M) = 0.18/0.55 = 0.3273

Type White Blue Black Red Total A 0.13 0.10 0.11 0.11 0.45 M 0.15 0.07 0.15 0.18 0.55 Total 0.28 0.17 0.26 0.29 1

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