(5 points) A random sample of adult drivers was obtained where 50% were men and 49% were women. Note that everyone is not classified as a ma

Question

(5 points) A random sample of adult drivers was obtained where 50% were men and 49% were women. Note that everyone is not classified as a man or a woman. A survey showed that 77% of the drivers rely on GPS systems. 38% of the drivers are men and use GPS while 38% of the drivers are women and use GPS. Suppose a person included in this survey is randomly selected. (0.5 pts.) a) Suppose the person selected is a man. What is the probability that he relies on a GPS system

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Thanh Hà 4 years 2021-08-05T03:21:57+00:00 1 Answers 9 views 0

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  1. mit
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    2021-08-05T03:23:40+00:00
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    Answer:

    the probabiility that the selected man relies on a GPS system is 0.494

    Step-by-step explanation:

    From the given information:

    Let X be the event that selected person is a man

    Let Y be the event that selected person is a woman

    Let Z be the event that selected relies or use GPS system.

    So;

    the following probabilities are:

    P(X) = 0.50

    P(Y) = 0.49

    P(Z) = 0.77

    P(X ∩ Z) = 0.38

    P(Y ∩ Z) = 0.38

    Now;

    if the selected person is a man, the probability that he relies on a GPS system can be determined as follows:

    P(Z|X) = \dfrac{P(X \cap Z)}{P(Z)}

    P(Z|X) = \dfrac{0.38}{0.77}

    \mathbf{P(Z|X) =0.494}

    Thus, the probabiility that the selected man relies on a GPS system is 0.494

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