Part 2: PROBLEMS. Show your work for an opportunity for partial credit. e c nd n

Question

Part 2: PROBLEMS. Show your work for an opportunity for partial credit. e c nd n W 1. (14 pts) A security company has installed two alarm systems in a building. Based on the manufacturer an re nc specifications, they believe that each system has a 20% risk of failure and that the systems operate independently of each other. This information can be used to partially develop this probability table. First System Works Fails Total Works .80 Second System Fails .20 Total .80 .20 1.00 Using this information, answer the following. (It may be helpful to complete the probability table before trying to answer the questions). a) Find the probability that the first system fails and the second system works. b) Find the probability that at least one of the two systems works. (HINT: "At least one works" is the same as "the first works or the second works'").

Explanation / Answer

from above being independent:

probability of any cell like first one for whcih first system works and second system work =(row toal*column total)

=0.8*0.8 =0.64

like wise:

a) from above probability that first system fails and second system works =0.16

b) probability that at least one of two system works =1-P(both system fails) =1-0.04 =0.96

first system works fails total second works 0.64 0.16 0.8 fails 0.16 0.04 0.2 total 0.8 0.2 1

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