6. For Design 3, consider the probability of a random individual in South Dorchester being sampled; and the probability of a random individual in Harbor Islands being sampled. These probabilities are approximately the same as the probabilities calculated using:

This is not a complete question.

To calculate the probability of a random individual in South Dorchester and Harbor Islands being sampled, we need some additional information. Specifically, we need the total population of each area and the sample size. Once we have this information, we can apply a basic probability formula to calculate the probabilities.

Let's assume we have the following information:

- Population of South Dorchester: P(SD)
- Population of Harbor Islands: P(HI)
- Sample size: S

The probability of a random individual in South Dorchester being sampled can be calculated using the formula:

P(SD being sampled) = S / P(SD)

Similarly, the probability of a random individual in Harbor Islands being sampled can be calculated using the formula:

P(HI being sampled) = S / P(HI)

If the probabilities for both areas are approximately the same, it means that the sample size is proportional to the population size in each area. In other words, if the ratios of the sample size to the populations are similar, then the probabilities will be approximately the same.

Note: The term "approximately" is used because we are assuming that the sampling is done randomly and independently, without any bias. In reality, there may be other factors that affect the sampling process and the probabilities.