Diseases I and II are prevalent among people in a certain population. It is assumed that 10% of the population will contract disease I sometime during their lifetime, 15%will contract disease II eventually, and 3% will contract both diseasesFind the probability that a randomly chosen person from this population will contract at least one disease.Find the probability that a randomly chosen person from this population will contract neither disease.Find the probability that a randomly chosen person from this population will contract disease I but not disease II.

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Asked Mar 28, 2019
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Diseases I and II are prevalent among people in a certain population. It is assumed that 10% of the population will contract disease I sometime during their lifetime, 15%will contract disease II eventually, and 3% will contract both diseases
Find the probability that a randomly chosen person from this population will contract at least one disease.
Find the probability that a randomly chosen person from this population will contract neither disease.
Find the probability that a randomly chosen person from this population will contract disease I but not disease II.

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Expert Answer

Step 1

Let Abe the event that a person will contract disease I sometime during their lifetime.

Let B be the event that a person will contract disease II sometime during their lifetime.

Hence, AC be the event that a person will not contract disease I anytime during their lifetime.

BC be the event that a person will not contract disease II anytime during their lifetime.

From the information,

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Step 2

The probability that a randomly chosen person from this population will contract at least one disease:

The complement of the above event is a randomly chosen person from this population will contract no disease.This event can be written as, 

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Step 3

Therefore, the probability that a randomly chosen person from this population will contract no disease is 0.78.

Therefore, by using the complement...

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