Three types of batteries are being tested type I type n and

Three types of batteries are being tested, type I, type n, and type HI. The outcome (I, II, HI) denotes that the battery of type I fails first, the battery of type II next, and the battery of type HI 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 H battery? (This problem is continued in Problem 1.4.9.)

Solution

a)

P(I last longest) = 0.39 + 0.03 = 0.42 [ANSWER]

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b)

P(I last shortest) = 0.11 + 0.07 = 0.18 [ANSWER]

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c)

P(I does not last longest) = 1 - P(I last longest)

= 1 - 0.42

= 0.58 [ANSWER]

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d)

P(I last longer than II) = 0.24 + 0.39 = 0.63 [ANSWER]