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Sagot :
Answer:
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.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
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 [tex]P(B) = 0.48[/tex]
For those who are 11 to 13 years of age, 54% have inadequate calcium intake.
This means that [tex]P(A|B) = 0.54[/tex]
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
[tex]P(A) = 0.17*0.52 + 0.54*0.48 = 0.3476[/tex]
Find the probability that a child from this population who has inadequate intake is 11 to 13 years old.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.48*0.54}{0.3476} = 0.7457[/tex]
0.7457 = 74.57% probability that a child from this population who has inadequate intake is 11 to 13 years old.
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