Question

question 9 of 25
the data give the average number of days in may that are clear and cloudy in two cities
on a day in may, what is the probability that it is clear, given that you are in san antonio? explain how you found the answer, and round your answer to two decimal places.
a. 0.26, because 6 of the 23 days were clear
b. 0.10, because 6 of the 60 days were clear

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of frequency - based probability (using the table data), if \(A\) is the event "clear" and \(B\) is the event "in San Antonio", then \(P(A|B)=\frac{\text{Number of clear days in San Antonio}}{\text{Total number of days in San Antonio}}\)

Step2: Identify the relevant values from the table

From the table, the number of clear days in San Antonio is \(6\), and the total number of days in San Antonio (May has \(30\) days on average for each city in the table) is \(30\)

Step3: Calculate the probability

$$P=\frac{6}{30}=0.20$$

Option A is incorrect because it uses the total number of clear days (\(23\)) instead of the total number of days in San Antonio. Option B is incorrect because it uses the grand - total number of days (\(60\)) instead of the total number of days in San Antonio.

Answer:

C. \(0.20\), because \(6\) of the \(30\) days in San Antonio were clear