Problem 83 One of the common symptoms of Alzlieimers disease

Problem 8.3. One of the common symptoms of Alzlieimer^?s disease is the memory loss that disrupts daily life. This is just one of the 10 warning signs of Alzheimer^?s disease. Another frequently encountered sign consists in having difficulty to complete familiar tasks. In a large group of early stage Alzheimer patients, 85% of them experience memory loss, 78% have difficulty completing familiar tasks and 67% show both signs. (a) What is the probability that an early stage Alzheimer patient shows one of these signs? (b) What is the probability that an early stage Alzheimer patient does not show any of these two signs?

Solution

Let A = memory loss
B = difficulty in tasks

a)

P(one sign) = P(A only) + P(B only) = [P(A) - P(A and B)] + [P(B) - P(A and B)

= [0.85 - 0.67] + [0.78 - 0.67]

= 0.18 + 0.11

= 0.29 [ANSWER]

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b)

P(not A nor B) = 1 - P(A U B) = 1 - [P(A) + P(B) - P(A and B)]

= 1 - [0.85 + 0.78 - 0.67]

= 0.04 [ANSWER]