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A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?
  • a)
    22/133
  • b)
    23/133
  • c)
    27/133
  • d)
    25/133
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A laboratory blood test is 99% effective in detecting a certain diseas...
Let 
E1 and E2 are events that a person has disease and the person has not disease.
Let A  = event that the test result is positive






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Most Upvoted Answer
A laboratory blood test is 99% effective in detecting a certain diseas...
To solve this problem, we will use Bayes' theorem. Bayes' theorem allows us to update our beliefs about the probability of an event occurring based on new evidence.

Let's define the events:
A: The person has the disease.
B: The test result is positive.

We are given the following information:
P(A) = 0.001 (0.1% of the population actually has the disease)
P(B|A) = 0.99 (the test is 99% effective in detecting the disease)
P(B|not A) = 0.005 (the test yields a false positive for 0.5% of healthy people)

We are asked to find P(A|B), the probability that a person has the disease given that his test result is positive.

Applying Bayes' theorem, we have:
P(A|B) = (P(B|A) * P(A)) / P(B)

Calculating the values:
P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)
P(B) = 0.99 * 0.001 + 0.005 * (1 - 0.001)
P(B) = 0.00099 + 0.004995
P(B) = 0.005985

P(A|B) = (0.99 * 0.001) / 0.005985
P(A|B) = 0.00099 / 0.005985
P(A|B) ≈ 0.165

To simplify the answer, we can express it as a fraction:
P(A|B) ≈ 0.165
P(A|B) ≈ 165/1000
P(A|B) ≈ 33/200

The closest option to 33/200 is option A) 22/133.
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A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?a)22/133b)23/133c)27/133d)25/133Correct answer is option 'A'. Can you explain this answer?
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