A 2010 study in the journal Pediatric found that 8% of children under the age of

Question

A 2010 study in the journal Pediatric found that 8% of children under the age of 18 in the US have at least one food allergy. Among those with food allergies, 39% have a history of severe reaction.

(a) What is the probability that a child selected at random from this population has at least one food allergy and a history of severe reaction?

(b) It was also reported that 30% of those with an allergy are, in fact, allergic to multiple foods. If a child is randomly selected from this population, what is the probability that he or she is allergic to multiple foods?

Explanation / Answer

Let A : Child under 18 have at least 1 food allergy

B : Have severe reaction

a) P(Child selected at random has at least one food allergy and history of severe reaction),

Using rule : P(A and B) = P(A) * P(B)

We have,

P(At least 1 food allergy) = 0.08

P(History of severe reaction) = 0.39

P(At least 1 food allergy anf history of severe reaction) = P(At least 1 food allergy) * P(History of severe reaction)

= 0.08 * 0.39

= 0.0312

b) From given data,

P(allergy) = 0.08

P(multiple food allergy) = 0.3

P( allergy and multiple food allergy) = P(allergy) * P(multiple food allergy)

=0.08 * 0.3

= 0.024

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