I am at my office AND not working 2\%2% of the time. I am at my office 10\%10% of the time. What is the conditional probability that I am no

Question

I am at my office AND not working 2\%2% of the time. I am at my office 10\%10% of the time. What is the conditional probability that I am not working, if I am at my office?

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Maya 2 weeks 2021-09-09T13:29:10+00:00 1 Answer 0

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    2021-09-09T13:31:05+00:00

    Answer:

    20% conditional probability that I am not working, if I am at my office

    Step-by-step explanation:

    Conditional probability formula:

    P(B|A) = \frac{P(A \cap B)}{P(A)}

    In which

    P(B|A) is the probability of event B happening, given that A happened.

    P(A \cap B) is the probability of both A and B happening.

    P(A) is the probability of A happening.

    In this question:

    Event A: Being at the office.

    Event B: Not working.

    I am at my office AND not working 2% of the time.

    This means that P(A \cap B) = 0.02

    I am at my office 10% of the time.

    This means that P(A) = 0.1

    What is the conditional probability that I am not working, if I am at my office?

    P(B|A) = \frac{P(A \cap B)}{P(A)}

    P(B|A) = \frac{0.02}{0.1}

    P(B|A) = 0.2

    20% conditional probability that I am not working, if I am at my office

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