Question

The probability that a person has a certain disease is 0.04. 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 0.02. 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? The probability is 0.036. (Round to three decimal places as needed.)

          The probability that a person has a certain disease is 0.04. 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 0.02.
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?
The probability is 0.036.
(Round to three decimal places as needed.)

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The probability that a person has a certain disease is 0.04. 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 0.02.
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?
The probability is 0.036.
(Round to three decimal places as needed.)

Added by Kevin T.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Joanna Quigley

10/15/2022

Step 1

Given: - Probability of having the disease = 0.04 - Probability of testing positive if the disease is present = 0.92 - Probability of testing positive if the disease is not present = 0.02 Calculate the overall probability of testing positive: \[ (0.04 \times Show more…

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The probability that a person has a certain disease is 0.04. 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 0.02. 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? The probability is 0.036. (Round to three decimal places as needed.)

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Transcript

00:01 The probability of having a particular disease is 0 .04.

00:04 So we're going to have probability of having this disease, d, 0 .04.

00:11 Okay, and we have a lot of information on it.

00:14 I'm just going to try and turn it all into probability notation to make it clearer.

00:18 So we have a test.

00:20 If the disease is present, the probability of a positive result is 0 .92.

00:25 So probability of a positive result, given that they have the disease is 0 .92.

00:31 If they don't have the disease, the probability of a positive result is 0 .02.

00:38 So probability positive given no disease is not.

00:43 Okay, so a positive result is received.

00:48 What's the probability they actually have the disease? so we want the probability of having the disease given a positive result.

00:58 Great, so we've turned this paragraph into our probability notation, and when you want to switch around the conditional probability like this, you use bay's rule.

01:09 There's a formula to help us.

01:13 So we're using bay's rule, and the formula is that the probability of b given a is equal to the probability of a multiplied by the probability of b divided by the probability of a.

01:32 So let's apply that to this particular case.

01:34 Make some space for it.

01:43 So we need the probability of positive given disease, which we have.

01:49 We need the probability of having the disease, which we have...

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