Question

A dealer sells two brands of new cars. One, C, is of primarily American origin; the other, the G, is primarily Japanese. The dealer makes warranty repairs for both brands and classifies jobs according to the primary problem to be corrected. If in any case there is more than one problem, each one is noted in a separate list. Last year's records indicate the following numbers for the reported problems:

Problem:

		Motor	Transmision	Escape	Armed	Other	Total
Brand	C	106	211	67	133	24	541
Brand	G	21	115	16	24	6	182
	Totals	127	326	83	157	30	723

1. What is the problem that a randomly selected problem corresponds to the C mark?
2. Problems related to the engine or transmission are serious. What is the probability that a randomly selected problem is serious?
3. What is the probability that a randomly selected problem corresponds to the C mark given that it is a transmission problem.

Answer 1

a) P(C mark) = Total brand C / Grand Total = 541 / 723 = 0.7483

b) P(problem is serious) = P(Motor) + P(Transmission) = 127/723 + 326/723 = 0.6266

c) P(C mark | transmission) = P(C mark and transmission) / P(transmission)

                                            = (211/723) / (326/723)

                                            = 211 / 326

                                            = 0.6472