Answer: 0.9762
Step-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
