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5 August, 11:37

Successful implementation of a new system is based on three independent modules. Module 1 works properly with probability 0.9, Module 2 works properly with probability 0.84, and Module 3 works properly with probability 0.65. What is the probability that at least one of these three modules will fail to work properly?

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  1. 5 August, 15:30
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    The probability is 0.5086

    Step-by-step explanation:

    The probability P that at least one of these three modules will fail to work properly is calculated as:

    P = 1 - P'

    Where P' is the probability that all the modules works properly. So, P' os calculated as:

    P' = 0.9 * 0.84 * 0.65

    P' = 0.4914

    Because 0.9 is the probability that module 1 works properly, 0.84 is the probability that module 2 works properly and 0.65 is the probability that module 3 works properly.

    Finally, the probability P that at least one of these three modules will fail to work properly is:

    P = 1 - 0.4914

    P = 0.5086
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