Question

For the month of March in a certain city, 57% of the days are cloudy. Also in the month of March in the same city, 55% of the days are cloudy and rainy. What is the probability that a randomly selected day in March will be rainy if it is cloudy?

Answer 1

Answer: 0.9649

Step-by-step explanation:

Let A denote the event that the days are cloudy and B denotes the event that the days are rainy.

Given : For the month of March in a certain city, the probability that days are cloudy :$P(A)=0.57$

Also in the month of March in the same city,, the probability that the days are cloudy and rainy :$P(A\cap B)=0.55$

Now by using the conditional probability, the probability that a randomly selected day in March will be rainy if it is cloudy will be :-

$P(B|A)=\dfrac{P(A\cap B)}{P(A)}$

$\Rightarrow\ P(B|A)=\dfrac{0.55}{0.57}\\\\=0.964912280702\approx0.9649\ \ \text{[Rounded to four decimal places.]}$

Hence, the probability that a randomly selected day in March will be rainy if it is cloudy = 0.9649