Question

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​?

Answer 1

30.64%

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%