Refer to the table which summarizes the results of testing for a certain disease

Question

Refer to the table which summarizes the results of testing for a certain disease. one of the results is randomly selected, what is the probability that it is a false nogative (test indicates the person does not have the disease when in fact they do)? Round to the nearest thousandth. What does this probability suggest about the accuracy of the test? 0.039; The probability of this error is low so the test is fairly accurate. 0.581; The probability of this error is high so the test is not very accurate 0.019; The probability of this error is low so the test is fairly accurate 0 049; The probability of this error is low so the test is fairly accurate.

Explanation / Answer

Given:

X = 117, 6, 12, 173.

X = 117 + 6 + 12 + 173

       = 308

     = n(S), total number of events.

Let A be the event that ‘the result is false negative’

So the number of favorable event is n(A) =173

[Given: a person have a disease but the test indicates a person does not have a disease]

The probability that the result is a false negative is

P(A)=n(A)/n(S)

=173/308

=0.561

This probability suggest that the test is not very accurate. since, it is false negative

That is, The probability of this error is high so the test is not very accurate.

Hence the correct answer is ‘choice B’

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