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13 November, 15:00

For the month of MarchMarch in a certain city, the probability that the weather on a given day is cloudycloudy is 0.620.62. Also in the month of MarchMarch in the same city, the probability that the weather on a given day is cloudycloudy and foggyfoggy is 0.190.19. What is the probability that a randomly selected day in MarchMarch will be foggyfoggy if it is cloudycloudy ?

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  1. 13 November, 17:16
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    30.64%

    Step-by-step explanation:

    We must find the probability that foggy if it is cloudy, that is P (foggy | cloudy)

    We have the probability that this foggy and coudy is 0.19

    P (foggy and coudy) = 0.19

    The probability that this cloudy is 0.62, P (cloudy) = 0.62

    P (foggy | cloudy) = P (foggy and coudy) / P (cloudy)

    replacing:

    P (foggy | cloudy) = 0.19 / 0.62

    P (foggy | cloudy) = 0.3064

    that is to say that the probability that foggy if it is cloudy is 30.64%
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