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Alexandra [31]
3 years ago
8

medical tests. Task Compute the requested probabilities using the contingency table. A group of 7500 individuals take part in a

survey about a rare disease and medical test. The data for the group is given in the table below. A person listed as "Sick" has the disease, while someone listed as "Not Sick does not "Tested Positive means the test indicated the person was sick, and "Tested Negative" means the test indicated they were not sick. The test is believed to be around 99% accurate. Sick Not Sick Tested Positive 59 75 Tested Negative 1 7365 h One person at random is chosen from the group (3 pts) Find the probability the person is sick. b. (3 pts) Find the probability the test is positive given that the person is sick (3 pts) Find the probability the test is negative given that the person is not sick. d. (pts) Find the probability the person is sick given that the test is positive (3 pts) Find the probability the person is not sick given that the test is negative. f. (5 pts) When we say a test is 99% accurate, to what is that referring? Given vour calculations, should information other than a single test be considered when diagnosing a rare condition? If so, what other information might be considered? Criteria for Success​

Mathematics
1 answer:
uysha [10]3 years ago
4 0

Probabilities are used to determine the chances of an event

  • The probability that a person is sick is: 0.008
  • The probability that a test is positive, given that the person is sick is 0.9833
  • The probability that a test is negative, given that the person is not sick is: 0.9899
  • The probability that a person is sick, given that the test is positive is: 0.4403
  • The probability that a person is not sick, given that the test is negative is: 0.9998
  • A 99% accurate test is a correct test

<u />

<u>(a) Probability that a person is sick</u>

From the table, we have:

\mathbf{Sick = 59+1 = 60}

So, the probability that a person is sick is:

\mathbf{Pr = \frac{Sick}{Total}}

This gives

\mathbf{Pr = \frac{60}{7500}}

\mathbf{Pr = 0.008}

The probability that a person is sick is: 0.008

<u>(b) Probability that a test is positive, given that the person is sick</u>

From the table, we have:

\mathbf{Positive\ and\ Sick=59}

So, the probability that a test is positive, given that the person is sick is:

\mathbf{Pr = \frac{Positive\ and\ Sick}{Sick}}

This gives

\mathbf{Pr = \frac{59}{60}}

\mathbf{Pr = 0.9833}

The probability that a test is positive, given that the person is sick is 0.9833

<u>(c) Probability that a test is negative, given that the person is not sick</u>

From the table, we have:

\mathbf{Negative\ and\ Not\ Sick=7365}

\mathbf{Not\ Sick = 75 + 7365 = 7440}

So, the probability that a test is negative, given that the person is not sick is:

\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Not\ Sick}}

This gives

\mathbf{Pr = \frac{7365}{7440}}

\mathbf{Pr = 0.9899}

The probability that a test is negative, given that the person is not sick is: 0.9899

<u>(d) Probability that a person is sick, given that the test is positive</u>

From the table, we have:

\mathbf{Positive\ and\ Sick=59}

\mathbf{Positive=59 + 75 = 134}

So, the probability that a person is sick, given that the test is positive is:

\mathbf{Pr = \frac{Positive\ and\ Sick}{Positive}}

This gives

\mathbf{Pr = \frac{59}{134}}

\mathbf{Pr = 0.4403}

The probability that a person is sick, given that the test is positive is: 0.4403

<u>(e) Probability that a person is not sick, given that the test is negative</u>

From the table, we have:

\mathbf{Negative\ and\ Not\ Sick=7365}

\mathbf{Negative = 1+ 7365 = 7366}

So, the probability that a person is not sick, given that the test is negative is:

\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Negative}}

This gives

\mathbf{Pr = \frac{7365}{7366}}

\mathbf{Pr = 0.9998}

The probability that a person is not sick, given that the test is negative is: 0.9998

<u>(f) When a test is 99% accurate</u>

The accuracy of test is the measure of its sensitivity, prevalence and specificity.

So, when a test is said to be 99% accurate, it means that the test is correct, and the result is usable; irrespective of whether the result is positive or negative.

Read more about probabilities at:

brainly.com/question/11234923

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