Attached is a table showing the prevalence of Alzheimer's disease.
Suppose an unrelated 77 year old man, 76 year old woman, and 82 year old woman are selected from a community.
1. What is the probability that all three of these individuals have Alzheimer's disease?
2. What is the probability that at least one of the three people has Alzheimer's disease?
3. Suppose we know one of the three people has Alzheimer's disease, but we don't know which one. What is conditional probability that the affected person is a woman?
1. According to the chart, the probability that 77 year old man has the disease (hebelongs to the male age group 75-79) P1=4.9%
The probability that 76 year old woman has the disease (she belongs to the female age group 75-79) P2=2.3%
The probability that 82 year old woman has the disease (she belongs to the female age group 80-84) P3=7.8%
Since these three events are independent, the total probability of all three having the disease P=P1*P2*P3=4.9%*2.3%*7.8%=0.000087906
2. There ...
The solution provides detailed explanation how to solve probability of independent events and find the conditional probability.