For the month of January in a certain city, 42% of the days are cloudy. Also in the month of January in the same city, 41% of the days are cloudy and rainy. What is the probability that a randomly selected day in January will be rainy if it is cloudy?
Accepted Solution
A:
Answer: 0.9762Step-by-step explanation:Let A be the event that days are cloudy and B be the event that days are rainy for January month .Given : The probability that the days are cloudy = [tex]P(A)=0.42[/tex]The probability that the days are cloudy and rainy = [tex]P(A\cap B)=0.41[/tex]Now, the conditional probability that a randomly selected day in January will be rainy if it is cloudy is given by :-[tex]P(B|A)=\dfrac{P(B\cap A)}{P(A)}\\\\\Rightarrow\ P(B|A)=\dfrac{0.41}{0.42}=0.97619047619\approx0.9762[/tex]Hence, the probability that a randomly selected day in January will be rainy if it is cloudy = 0.9762