Final answer:
The probability that a randomly selected household earns $75,000 or more per year, given that it is in a certain region, is calculated using the formula for conditional probability. The result is approximately 38.6%.
Step-by-step explanation:
The question asks to determine the probability that a randomly selected household earns $75,000 or more per year, given that the house is in a certain region.
We have two pieces of data from a survey: 22.3% of households are in that region, and 8.6% of all households earn $75,000 or more per year and are located in the same region.
To find the conditional probability, we use the definition: P(A given B) = P(A and B) / P(B).
Here, let A be the event that a household earns $75,000 or more per year, and B be the event that a household is in that region. We have P(A and B) = 8.6% and P(B) = 22.3%. So, P(A given B) = (8.6%) / (22.3%).
After calculating, we get P(A given B) = 0.3856502242 or about 38.6% when rounded to one decimal place.
Hence, the probability that a randomly selected household earns $75,000 or more per year, given that it is in the certain region, is 38.6%.