Question

A maintenance firm has gathered the following data regarding the failure of air conditioning systems:

	Gas Leak	No Gas Leak
Electrical Failure	70	30
No Electrical Failure	40	10

a) What is the probability that there is an electrical failure given that there was a gas leak? (show work)

b) What is the probability that there is a gas leak given that there was an electrical failure?

c) Are the events “electrical failure” and “gas leak” independent? Justify your answer.

Answer 1

Total = 70 + 40 + 30 + 10 = 150

a) P(electrical failure | gas leak) = P(electrical failure and gas leak) / P(gas leak)

                                                    = (70/150) / ((70+40)/150)

                                                    = 70/110

                                                    = 7/11 or 0.6364

b) P(gas leak | electrical failure) = P(gas leak and electrical failure) / P(electrical failure)

                                                    = (70/150) / ((70+30)/100)

                                                    = 70/100

                                                    = 7/10 or 0.7

c) P(electrical failure) = (70 + 30) / 150 = 0.67

Since, P(electrical failure | gas leak) is not equal to P(electrical failure), they are not independent events.