Questions: A taste test asks people from Texas and California which pasta they prefer, brand A or brand B. This table shows the results. Brand A Brand B Total ------------------------------------ Texas 80 45 125 California 90 60 150 Total 170 105 275 A person is randomly selected from those tested. What is the probability that the person is from California, given that the person prefers brand A? Round your answer to two decimal places. A. 0.62 B. 0.55 C. 0.53 D. 0.60

Solution Steps

We are given a table with the number of people from Texas and California who prefer either brand A or brand B. We need to find the probability that a person is from California, given that they prefer brand A.

The formula for conditional probability is:

\[ P(\text{California} \mid \text{Brand A}) = \frac{P(\text{California and Brand A})}{P(\text{Brand A})} \]

• \(P(\text{California and Brand A})\) is the probability that a person is from California and prefers brand A. From the table, this is the number of people from California who prefer brand A, which is 90.
• \(P(\text{Brand A})\) is the probability that a person prefers brand A. From the table, this is the total number of people who prefer brand A, which is 170.

Substitute the values into the formula:

\[ P(\text{California} \mid \text{Brand A}) = \frac{90}{170} \approx 0.5294 \]

Round the result to two decimal places:

\[ P(\text{California} \mid \text{Brand A}) \approx 0.53 \]

Final Answer