Respuesta :
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
[tex]P(A)=53\%=0.53,\\\\P(A\cap B)=46\%=0.46.[/tex]
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
[tex]P(B/A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{0.46}{0.53}=0.87=87.79\%.[/tex]
Thus, the required probability that a randomly selected day in November will be snowy if it is cloudy is 87.79%.
