Three elderly subjects are randomly selected and screened for Alzheimer’s diseas

Question

Three elderly subjects are randomly selected and screened for Alzheimer’s disease:

Subject 1 = Male, age 77

Subject 2 = Female, age 76   

Subject 3 = Female, age 82

Recognize that each subject either has A.D. or does not. These leaves us with two possible outcomes for each subject. Let’s label the outcomes of interest with short simple terms that are easy to understand and keep track of:

1. 1st  = Subject 1 has A.D.       Not 1st  = subject 1 does not have A.D.

2nd = Subject 2 has A.D. Not 2nd = subject 2 does not have A.D.

3rd = Subject 3 has A.D. Not 3rd  = subject 3 does not have A.D.

2. True or False? Considering that A.D. is not contagious and our subjects are randomly selected from an enormous population, the probability that one subject has Alzheimer’s disease is conditional on whether or not another subject has Alzheimer’s disease.

3. What is the probability that all three subjects have Alzheimer's Disease?

4. What is the probability that at least one of the randomly selected women has Alzheimer's disease?

Below is a table showing the percentage of elderly people who develop Alzheimer's disease (A.D.) in the United States (adapted from Fundamentals of Biostatistics, Rosner 2011): Males with Females with Group 5-69 1.6 % 0-74 5-79 0% 2% 3% 8% 9% 80-84 6% Three elderly subjects are randomly selected and screened for Alzheimer's disease: Subject 1- Male, age 77 Subject 2 = Female, age 76 Subject 3 Female, age 82

Explanation / Answer

2.

False, it should not be conditional.

3.

P(M77)=0.049, P(F76)=0.023, P(F82)=0.078. Probability that all the three have Alzheimer's disease=

4.

P(F76)orP(F82)=P(F76)+P(F82)-{P(F76)*P(F82)}

=0.023+0.078-{0.023*0.078}

=0.099206

(0.049*0.023*0.078)=0.000087906.

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