In the population of young children eligible to participate in a study of whethe

Question

In the population of young children eligible to participate in a study of whether or not their calcium intake is adequate, 54% are 5 to 10 years of age and 46% are 11 to 13 years of age. For those who are 5 to 10 years of age, 16% have inadequate calcium intake. For those who are 11 to 13 years of age, 59% have inadequate calcium intake.

a) Use Bayes's rule to find (± 0.001) the probability that a child from this population who has inadequate intake is 11 to 13 years old:

P( 11 to 13 | inadequate calcium) =

Explanation / Answer

here probababilty of 5-10 =P(5-10)=0.54

and that of 11 to 13 years =P(11-13)=0.46

probabilty of inadequate calcium intake =P(IC) =P(5-10)*P(IC|5-10)+P(11-13)*P(IC|11-13) =0.54*0.16+0.46*0.59

=0.3578

hence probability that a child from this population who has inadequate intake is 11 to 13 years old =

P(11 to 13|IC)=P(11-13)*P(IC|11-13)/P(IC) =0.46*0.59/0.3578=0.7585

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