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 a two - way table for this problem, if \(A\) is the event that the day is clear and \(B\) is the event that the day is 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 is \(30\).

Step3: Calculate the probability

Using the formula \(P=\frac{6}{30}\). Simplifying \(\frac{6}{30}=\frac{6\div6}{30\div6}=\frac{1}{5} = 0.2\).

The error in option A is that it uses the total number of clear days (\(23\)) instead of the total number of days in San Antonio (\(30\)). The error in option B is that it uses the grand - total number of days (\(60\)) instead of the total number of days in San Antonio (\(30\)).

Answer:

None of the options are correct. The correct probability is \(0.2\), because \(6\) of the \(30\) days in San Antonio were clear.