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, 17% have inadequate calcium intake. For those who are 11 to 13 years of age, 54% 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.

0.7457 = 74.57% probability that a child from this population who has inadequate intake is 11 to 13 years old.

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Inadequate intake

Event B: Is 11 to 13 years old.

48% are 11 to 13 years of age.

This means that

For those who are 11 to 13 years of age, 54% have inadequate calcium intake.

This means that

Probability of inadequate calcium intake:

0.17 of 0.52(5 to 10 years old)

0.54 of 0.48(11 to 13 years old). So

Find the probability that a child from this population who has inadequate intake is 11 to 13 years old.

0.7457 = 74.57% probability that a child from this population who has inadequate intake is 11 to 13 years old.