Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
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
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
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.