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, 56 % have inadequate calcium intake.

Let A=A="5 to 10 years old" and Ac=Ac="11 to 13 years old" (these are the only two age groups under consideration).

Let C=C="adequate calcium intake" and Cc=Cc="inadequate calcium intake".

Calculate:

P(A)P(A) =

P(Ac)P(Ac) =

P(Cc|A)P(Cc|A) =

P(Cc|Ac)P(Cc|Ac) =

P(Cc)P(Cc) =

Answer 1

P(A) = P(age is 5 to 10 years ) = 0.52, Therefore 0.52 is the required probability here.

P(Ac) = 1 - P(A) = 1 - 0.52 = 0.48. Therefore 0.48 is the required probability here.

We are given here that For those who are 5 to 10 years of age, 19 % have inadequate calcium intake,

Therefore P(Cc | A) = 0.19. Therefore 0.19 is the required probability here.

Also, we are given here that: For those who are 11 to 13 years of age, 56 % have inadequate calcium intake,

Therefore P(Cc | Ac) = 0.56. Therefore 0.56 is the required probability here.

P(Cc) is computed using the law of total probability as:
P(Cc) = P(Cc | A)P(A) + P(Cc | Ac)P(Ac)

= 0.19*0.52 + 0.56*0.48 = 0.3676

Therefore 0.3676 is the required probability here.