Three types of batteries are being tested, type I, type II, and type III. The ou

Question

Three types of batteries are being tested, type I, type II, and type III. The outcome (I, II, III) denotes that the battery of type I fails first, the battery of type II next, and the battery of type III lasts the longest. The probabilities of the six outcomes are given in Figure 1.24. What is the probability that the type I battery lasts longest? the type I battery lasts shortest? the type I battery does not last longest? the type I battery lasts longer than the type II battery? (This problem is continued in Problem 1.4.9.) FIGURE 1.24 Probability values for battery lifetimes

Explanation / Answer

Battery I will last the longest for (III,II,I) and (II,III,I)- so sum these probabilities to get .39+.03 = .42
b) Battery I will last the shortest for (I,II,III) and (I,III,II)- so sum these probabilities to get .11+.07 = .18
c) Battery 1 will not last the longest for every time that doesnot apply to a, so it is 1-.42 = .58
d) Battery I lasts longer than II for whenever I lasts thelongest as well as (II,I,III) - sum these to get .42+.24 =.66
Hope that helps

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