Question

In the population of young children eligible to participate in a study of whether or not their calcium intake is adequate, 52% are 5 to 10 years of age and 48% are 11 to 13 years of age. For those who are 5 to 10 years of age, 19% have inadequate calcium intake. For those who are 11 to 13 years of age, 58% have inadequate calcium intake.

Use Bayes's rule to find the probability that a child from this population who has inadequate intake is 11 to 13 years old.

We will consider the sample space, S, as all of the children participating in the study. We are given that 52% are 5 to 10 years of age and 48% are 11 to 13 years of age.

If we let event A = {5 to 10 years of age}, then we have P(A) = .52

Question:

Since a child cannot be in both age groups at once, we define event A^C = _____ , and we have P(A^C) =____

Answer 1

Since, A = {5 to 10 years of age} thus we define the event A^C = {11 to 13 years of age} and we have P(A^C) = 0.48. [Answer]

Explanation : Since a child can either belong to the 5 to 10 years age group or 11 to 13 years age group and since A is the event that a child belongs to the 5 to 10 years age group thus the event A^C is the event of a child belonging to the 11 to 13 years age group. Moreover, we are given in the question that 48% of the children belong to the 11 to 13 years age group. Thus, P(A^C) = 0.48.

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