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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.

\begin{tabular}{|c|c|c|c|}
\hline & Clear & Cloudy & Total \\
\hline Sacramento, CA & 17 & 13 & 30 \\
\hline San Antonio, TX & 6 & 24 & 30 \\
\hline Total & 23 & 37 & 60 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To solve the problem of finding the probability that it is clear given that you are in San Antonio, we'll follow these steps:

1. Identify the relevant data from the table.
2. Formulate the probability in terms of the data.
3. Perform the calculation.
4. Round the result to two decimal places.

### Step 1: Identify the relevant data
From the table, we can extract the data specific to San Antonio, TX:
- Number of clear days in San Antonio: [tex]\( \text{clear\_San\_Antonio} = 6 \)[/tex]
- Total number of days observed in San Antonio: [tex]\( \text{total\_San\_Antonio} = 30 \)[/tex]

### Step 2: Formulate the probability
The probability of a clear day given that you are in San Antonio can be found using the formula:
[tex]\[ P(\text{Clear} | \text{San Antonio}) = \frac{\text{Number of clear days in San Antonio}}{\text{Total number of days in San Antonio}} \][/tex]

### Step 3: Perform the calculation
Plugging in the numbers from Step 1:
[tex]\[ P(\text{Clear} | \text{San Antonio}) = \frac{6}{30} \][/tex]
Now, simplify this fraction:
[tex]\[ P(\text{Clear} | \text{San Antonio}) = \frac{1}{5} = 0.2 \][/tex]

### Step 4: Round the result
Our calculation already results in 0.2, which is in two decimal places.

Thus, the probability that it is clear given that you are in San Antonio is [tex]\( 0.2 \)[/tex] or 20%.

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