Question

The probability that a person has a certain disease is 0.05. Medical diagnostic tests are available to determine whether the person actually has the disease. If the disease is actually present, the probability that the medical diagnostic test will give a positive result (indicating that the disease is present) is 0.92. If the disease is not actually present, the probability of a positive test result (indicating that the disease is present) is 0.04. a. If the medical diagnostic test has given a positive result (indicating that the disease is present), what is the probability that the disease is actually present? b. If the medical diagnostic test has given a negative result (indicating that the disease is not present), what is the probability that the disease is not present? a. The probability is

          The probability that a person has a certain disease is 0.05.
Medical diagnostic tests are available to determine whether the
person actually has the disease. If the disease is
actually present, the probability that the medical diagnostic
test will give a positive result (indicating that the disease
is present) is 0.92. If the disease is not
actually present, the probability of a positive test
result (indicating that the disease is present) is
0.04.
a. If the medical diagnostic test has given a positive
result (indicating that the disease is present), what
is the probability that the disease is actually present?
b. If the medical diagnostic test has given a negative
result (indicating that the disease is not present),
what is the probability that the disease is not present?
a. The probability is

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Added by Lourdes R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

06/22/2022

Step 1

- Calculate the probability of the disease being present given a positive test result using the formula: \[ P(d|t^+) = \frac{P(t^+|d) \times P(d)}{P(t^+|d) \times P(d) + P(t^+|d') \times P(d')} \] - Substitute the given values: \[ P(d|t^+) = \frac{0.92 \times Show more…

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The probability that a person has a certain disease is 0.05. Medical diagnostic tests are available to determine whether the person actually has the disease. If the disease is actually present, the probability that the medical diagnostic test will give a positive result (indicating that the disease is present) is 0.92. If the disease is not actually present, the probability of a positive test result (indicating that the disease is present) is 0.04. a. If the medical diagnostic test has given a positive result (indicating that the disease is present), what is the probability that the disease is actually present? b. If the medical diagnostic test has given a negative result (indicating that the disease is not present), what is the probability that the disease is not present? a. The probability is

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Transcript

00:01 In this question we take that d denotes the person has disease and d dash denotes the person has no disease.

00:15 T positive is taken for the medical test has positive result and t negative is taken for negative result.

00:31 So from here we are given probability for d is equal to 0 .05.

00:38 Probability of d bar, this is probability of d dash, is equals to 1 minus 0 .05.

00:46 So that means probability of d dash is equals to 0 .95.

00:52 And also we are given the probability for test results positive when the person has disease is equal to 0 .95.

01:02 And the probability of test result positive when person has no disease is equal to 0 .0 .0.

01:12 So now in a part of this question, we have to find the probability for d given t positive.

01:21 So for finding this, this is equals to probability d intersection d positive, t positive, divided by probability.

01:32 T positive given d multiplied with probability of the probability t positive given d dash multiplied with probability of d dash.

01:45 So from here we know that probability d intersection t positive is equal to probability t positive given d multiplied with probability of d.

01:57 So by putting this value in the above formula, we have probability d given t positive is equal to probability of t positive given d multiplied with probability of d and this divided by probability t positive given d multiplied with probability of d plus probability of t positive given d dash multiplied with probability of d dash by putting all the values here.

02:27 We have probability of d given t positive as equals to 0 .92 multiplied with 0 .05 divided by 0 .92 multiplied with 0 .05 plus 0 .04 multiplied with 0 .95...

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