Alright, let's solve this step-by-step.
First, let's organize the information given in the table:
[tex]\[
\begin{tabular}{|l|c|c|c|}
\hline & \text{Brand A} & \text{Brand B} & \text{Total} \\
\hline \text{Texas} & 80 & 45 & 125 \\
\hline \text{California} & 90 & 60 & 150 \\
\hline \text{Total} & 170 & 105 & 275 \\
\hline
\end{tabular}
\][/tex]
The question asks for the probability that a person is from California, given that they prefer Brand A. This can be found using the conditional probability formula:
[tex]\[
P(\text{California} | \text{Brand A}) = \frac{P(\text{California and Brand A})}{P(\text{Brand A})}
\][/tex]
We need the following pieces of information:
1. [tex]\( P(\text{California and Brand A}) \)[/tex]: the number of people from California who prefer Brand A.
2. [tex]\( P(\text{Brand A}) \)[/tex]: the total number of people who prefer Brand A.
From the table:
- The number of people from California who prefer Brand A is 90.
- The total number of people who prefer Brand A is 170.
Using these values in the conditional probability formula:
[tex]\[
P(\text{California} | \text{Brand A}) = \frac{90}{170}
\][/tex]
Now, let's calculate this fraction:
[tex]\[
\frac{90}{170} \approx 0.5294
\][/tex]
We are asked to round the answer to two decimal places. So, rounding 0.5294 to two decimal places:
[tex]\[
0.53
\][/tex]
Thus, the probability that a randomly selected person who prefers Brand A is from California is:
[tex]\(\boxed{0.53}\)[/tex]
So the correct answer is:
D. 0.53
