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Question Help For the month of MarchMarch in a certain​ city, 5757​% of the days are cloudycloudy. Also in the month of MarchMarch in the same​ city, 5555​% of the days are cloudycloudy and foggyfoggy. What is the probability that a randomly selected day in MarchMarch will be foggyfoggy if it is cloudycloudy​?

Respuesta :

Answer: There is probability of 96.4% that  a day in March will be foggy if it is a cloudy.

Step-by-step explanation:

Since we have given that

Probability of the days in March are cloudy = 57%

Probability of the cloudy days in March are foggy = 55%

Let A be the event of cloudy days in March.

Let B be the event of foggy days in March.

So, here,

P(A) = 0.57

P(A∩B) = 0.55

We need to find the probability that days are foggy given that it is cloudy.

We would use "Conditional probability":

[tex]P(B\mid A)=\dfrac{P(A\cap B)}{P(A)}=\dfrac{0.55}{0.57}=0.964=96.4\%[/tex]

Hence, There is probability of 96.4% that  a day in March will be foggy if it is a cloudy.

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