Question

According to a posting on a website subsequent to the death of a child who bit into a peanut, a certain study found that 6% of children younger than 18 in the United States have at least one food allergy. Among those with food allergies, about 43% had a history of severe reaction.

(a)

If a child younger than 18 is randomly selected, what is the probability that he or she has at least one food allergy and a history of severe reaction? (Enter your answer to four decimal places.)

(b)

It was also reported that 40% of those with an allergy in fact are allergic to multiple foods. If a child younger than 18 is randomly selected, what is the probability that he or she is allergic to multiple foods? (Enter your answer to three decimal places.)

Answer 1

Answer:

Given that:

According to a posting on a website subsequent to the death of a child who bit into a peanut, a certain study found that 6% of children younger than 18 in the United States have at least one food allergy. Among those with food allergies, about 43% had a history of severe reaction.

P(A) = 6%

P(A) = 6/100

P(A) = 0.06

P(B/A) = 43%

P(B/A) = 43/100

P(B/A) = 0.43

(a) If a child younger than 18 is randomly selected, what is the probability that he or she has at least one food allergy and a history of severe reaction?

We know that P(A and B)

= P(A) * P(B/A)

= 0.06*0.43

= 0.0258

The probability that he/she has last one food allergic and a history of severe reaction is 0.0258

b) It was also reported that 40% of those with an allergy in fact are allergic to multiple foods. If a child younger than 18 is randomly selected, what is the probability that he or she is allergic to multiple foods?

We know that

P(A) = 0.06

P(C/A) = 40%

P(C/A) = 40/100

P(C/A) = 0.40

The probability that he/she is allergic to multiple foods = 0.024