Final answer:
To find the probability of a simple random sample of size 2 from 5 households having a combined income of at least $100,000, one must count the number of qualifying pairs (4) out of all possible pairs (10), resulting in a probability of 4/10 or 40%.
Step-by-step explanation:
The question is about determining the probability that the sum of the incomes in a simple random sample of size n=2 from a population of 5 households will be at least $100,000. To calculate this, we must consider all possible pairs of households and the sum of their household incomes. There are 10 possible pairs when taking a sample of size 2 from a population of 5. Out of these 10 pairs, we must find those that have a combined income of at least $100,000 and then divide this number by 10 to get the probability.
The pairs of household incomes that add up to at least $100,000 are ($60,000, $100,000), ($50,000, $100,000), ($40,000, $100,000), and ($30,000, $100,000). That is 4 pairs out of the possible 10. Therefore, the probability is 4/10, which simplifies to 0.4 or 40%. The answer is (a) 4/10.