Answer: Option C
[tex]P=0.47[/tex]
Step-by-step explanation:
First we assign names to events:
Event T: The selected people are from Texas
Event A: The selected person prefers the A mark
Event B: The selected person prefers the B mark
Now notice in the table that the total number of people is: 275.
Then, the number of people who prefer the A mark is: 170
The number of people who are from Texas is: 125
The number of people who are from Texas and who prefer the A brand is: 80
With this information we can obtain the following probabilities:
[tex]P (T\ and\ A) = \frac{80}{275} = \frac{16}{55}\\\\P (A) = \frac{170}{275} = \frac{34}{55}[/tex]
In this problem we look for the probability that a selected person will be texas since he prefers the A mark
This is:
[tex]P(T|A) = \frac{P(T\ and\ A)}{P(A)}\\\\P(T|A) = \frac{\frac{16}{55}}{\frac{34}{55}}=\frac{8}{17}\\\\P(T|A) =0.47[/tex]
