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18 July, 22:34

The probability that a machine works on a given day is based on whether it was working in the previous day. If the machine was working yesterday, then the probability it will work today is 0.76. Of the machine was broken yesterday, then the probability it will be broken today is 0.33. Of the machine is broken today, what is the likelihood that it will be working two days from now

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  1. 18 July, 22:38
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    73.03% probability that it will be working two days from now

    Step-by-step explanation:

    The machine is broken today.

    If the machine is broken on a day, the following day, it has a 1-0.33 = 0.67 probability of working on the next day.

    Otherwise, if it is works correctly on a day, it has a 0.76 probability of working on the next day.

    Uf the machine is broken today, what is the likelihood that it will be working two days from now

    Either of these outcomes are acceptable:

    Tomorrow - 2 days from now

    Not working - working

    Working - Working

    Not working - working

    Today, it does not work. So tomorrow the probability of not working correctly is 0.33. Then, if tomorrow does not work, 0.67 probability of working correctly two days from now

    0.33*0.67 = 0.2211

    Working - Working

    Today, it does not work. So tomorrow the probability of working correctly is 0.67. Then, if tomorrow works, 0.76 probability of working correctly two days from now

    0.67*0.76 = 0.5092

    Total

    0.2211 + 0.5092 = 0.7303

    73.03% probability that it will be working two days from now
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