According to a posting on a website subsequent to the death of a child who bit into a peanut, a certain study found that 7% of children younger than 18 in the United States have at least one food allergy. Among those with food allergies, about 41% 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 30% 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.)

Question

Mathematics

Karina Weiss

14 February, 21:43

According to a posting on a website subsequent to the death of a child who bit into a peanut, a certain study found that 7% of children younger than 18 in the United States have at least one food allergy. Among those with food allergies, about 41% 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 30% 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.)

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Answers (1)

Know the Answer?

Lawson Gordon · Answer 1

a.) 0.0287

b.) 0.020

Step-by-step explanation:

If a child is selected at random,

Probability of having at least one food allergy = 0.07

Probability of not having allergy = 0.93

If a child has at least one food allergy, probability of having a history of severe reaction = 0.41

If a child has at least one food allergy, probability of NOT having a history of severe reaction = 0.59

If a, child has at least one food allergy, probability of having multiple allergies = 0.3

For question a,

If a child is selected at random, the probability of having at least one food allergy and having a history of severe reaction = 0.07 * 0.41 = 0.0287 (4 d. p)

For question b,

If a child is selected at random, the probability of having multiple allergies is in two cases:

Either this child has multiple allergies with history of severe reaction OR the child Has multiple allergies with no history of severe reaction.

For the first case, when the child has an history of severe reaction, probability of having multiple allergies = 0.07 * 0.41 * 0.3 = 0.00861

For the Second case, when the child does not have an history of severe reaction, probability Of having multiple allergies = 0.07 * 0.53 * 0.3 = 0.01113

Probability of the child having multiple allergies = 0.00861 + 0.01113 = 0.01974 = 0.020 (3d. p)