A certain test is used to screen for Alzheimers disease. People with and without the disease were sampled and the following table resulted. Given the general Alzheimer disease rate is 0.001, what is the probability that a randomly selected individual will have an erroneous test result? [Hint: an error occurs if the individual has the disease and receives a negative test result or…?]

Test Disease No Disease Total
+ 436 5 441
- 14 495 509
Total 450 500 950

Question

A certain test is used to screen for Alzheimers disease. People with and without the disease were sampled and the following table resulted. Given the general Alzheimer disease rate is 0.001, what is the probability that a randomly selected individual will have an erroneous test result? [Hint: an error occurs if the individual has the disease and receives a negative test result or…?]

Test       Disease        No Disease          Total 
  +            436                 5                   441 
   -             14               495                509 
Total         450              500                 950

kropot72 · Answer

Let P(A) = probability that the individual has the disease and receives a false negative result.
$$P(A)=0.001\times \frac{5}{441}$$
Let P(B) = probability that the individual does not have the disease and receives a false positive result.
$$P(B)=(1-0.001)\times \frac{14}{509}=0.999\times \frac{14}{509}$$
Event A and event B cannot happen together therefore the events are mutually exclusive.
P(A or B) = P(A) + P(B) = probability of an erroneous test result.

anonymous · Answer

i don't get the right answer. the answer should be 0.010021

kropot72 · Answer

@Zarkon

kropot72 · Answer

@UnkleRhaukus

anonymous · Answer

????????

kropot72 · Answer

There is only 1 chance in 1000 that a randomly selected individual has the disease. Assuming that the individual does not have the disease and is tested, the probability of a false positive (based on the sampling result) is 14/509 = 0.0275.
The probability that a randomly selected selected individual has the disease and gives a false negative will add to the value of 0.0275.

Assuming that the question has been stated with no errors, I must conclude that the answer 0.010021 is incorrect. Have you any other way of checking the answer?

anonymous · Answer

well, maybe. i was told the answer was 0.010021. that's okay. i will skip this question

unklerhaukus · Answer

@kropot72, your woking is great, i think you just read the table wrong 
 ( its a trick table to read )

$$P(A)=0.001\times\frac{14}{450}\approx0.000031$$
$$P(B)=(1-0.001)\times\frac5{500}\approx0.00999$$

kropot72 · Answer

@UnkleRhaukus Thank you for your help. Your reading of the table sure gets the given correct answer. With more thought I am sure I will get my head around the correct reading of the table :)

anonymous · Answer

thank you. that makes more sense