Final answer:
The proportion of children not at risk who would pass follow-up testing depends on the test's specificity, calculated as 100% minus the Type I error rate. For screening with a 10 percent Type I error rate, 90% of children not at risk would be expected to pass follow-up testing.
Step-by-step explanation:
To address this, it's important to consider both Type I and Type II errors related to the screening. A Type I error occurs when the screening incorrectly identifies someone as at risk (false positive), and a Type II error refers to failing to detect the condition when it is present (false negative). According to the provided information, the screening has a 10 percent probability of a Type I error and a 20 percent probability of a Type II error. If we are interested in the proportion of children not at risk who pass follow-up testing, we are considering the test's specificity, which is the ability of the test to correctly identify those without the condition. Assuming a hypothetical population of 100 children, if all children were truly not at risk and the test has 90 percent specificity (100 percent minus the 10 percent Type I error), we would expect that 90 of these children correctly pass the follow-up testing as not having the condition.