Question

The following table summarizes results from 985 pedestrian deaths that were caused by accidents (based on data from the National Highway Traffic Safety Administration).

If the pedestrian was intoxicated, find the probability that the driver was intoxicated. Round to two decimals.

	pedestrian intoxicated
		yes	no
driver intoxicated	yes	59	79
	no	266	581

Answer 1

The data is given in the table below.

		Pedestrian Intoxicated	Total
		Yes	No
Driver Intoxicated	Yes	59	79	138
No	266	581	847
Total	325	660	985

P(driver was intoxicated | pedestrian was intoxicated) = P(driver and pedestrian were intoxicated) / P(pedestrian was intoxicated)       ............(conditional probability)

P(driver and pedestrian were intoxicated) = 59 / 985                                                             

P(pedestrian was intoxicated) = 325 / 985

P(driver was intoxicated | pedestrian was intoxicated) = (59 / 985) / (325 / 985)

                                                                                          = 59 / 325

                                                                                          = 0.1815

Therefore, if the pedestrian was intoxicated, the probability that the driver was intoxicated is 0.18