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10 July, 17:07

There are three workstations available having steady-state probabilities of 0.99, 0.95, 0.85 of being available on demand. What is the probability that at least two of the three will be available at any given time?

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  1. 10 July, 19:49
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    99.065% probability that at least two of the three will be available at any given time.

    Step-by-step explanation:

    We have these following probabilities:

    99% probability of the first workstation being available

    95% probability of the second workstation being available

    85% probability of the third workstation being avaiable

    Two being available:

    We can have three outcomes

    First and second available, third not. So

    0.99*0.95*0.15 = 0.141075

    First and third available, second not. So

    0.99*0.05*0.85 = 0.042075

    Second and third available, first not. So

    0.01*0.95*0.85 = 0.008075

    Adding them all

    P (2) = 0.141075 + 0.042075 + 0.008075 = 0.191225

    Three being available:

    P (3) = 0.99*0.95*0.85 = 0.799425

    What is the probability that at least two of the three will be available at any given time?

    P = P (2) + P (3) = 0.191225 + 0.799425 = 0.99065

    99.065% probability that at least two of the three will be available at any given time.
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