Transportation Quarterly (Jan. 1993) identified several studies on truck accidents that utilized misleading or inappropriate probability analysis. Consider the following excerpt from the article.* Can you find the flaw in the probability argument? For example, consider a situation where only two vehicle types are present in the traffic mix: trucks at 20% and cars at 80% of the total. If only two vehicle accidents are considered, the probability of occurrence for all events in the sample space would be as follows:

P (truck impacting truck) = P1TT2 = .20 × .20 = .04    

P (truck impacting car) = P1TC2 = .20 × .80 = .16

P (car impacting truck) = P1CT2 = .80 × .20 = .16

P (car impacting car) = P1CC2 = .80 × .80 = .64/100

Many analysts [used the calculation P(TT) + P(TC) + P(CT) = .36  to conclude] that trucks, constituting 20% of the traffic, are involved in 36% of all two-vehicle accidents. Hence cars, which constitute 80% of the traffic, are involved in 100% - 36% = 64% of the accidents.