Question

For the month of November in a certain​ city, 53​% of the days are cloudy. Also in the month of November in the same​ city, 46​% of the days are cloudy and snowy. What is the probability that a randomly selected day in November will be snowy if it is cloudy​?

Answer 1

Answer: The required probability that a randomly selected day in November will be snowy if it is cloudy​ is 86.79%.

Step-by-step explanation: Given that for the month of November in a certain city, 53​% of the days are cloudy. Also in the month of November in the same​ city, 46​% of the days are cloudy and snowy.

We are to find the probability that a randomly selected day in November will be snowy if it is cloudy​.

Let A denote the event that the day is cloudy and B denote the event that the day is snowy.

Then, according to the given information, we have

`P(A)=53\%=0.53,\\\\P(A\cap B)=46\%=0.46.`

Now, we need to find the conditional probability of event B given that the event A has already happened.

That is, P(B/A).

We know that

`P(B/A)=(P(B\cap A))/(P(A))=(0.46)/(0.53)=0.87=87.79\%.`

Thus, the required probability that a randomly selected day in November will be snowy if it is cloudy​ is 87.79%.