A test has been developed that is supposed to detect a disease in children. The

Question

A test has been developed that is supposed to detect a disease in children. The disease only occurs in 1 of every 2,000 children. Test results will be either "positive" or "negative". A "positive" test is correct 98% of the time. That is, if a child has the disease, the test will be "positive" with probability .98. A "negative" test is correct 95% of the time. That is, if a child does not have the disease, the test will be "negative" with probability equal to .95. Define all events in words here: Determine all probabilities given in the wording of the problem here: A child is tested and the result comes back as "positive". What is the probability that the child has the disease? Place a box around your final answer and express it to four decimal places.

Explanation / Answer

Solution :-

1. All events in words,

Event A: The child has the disease.

Event A': The child does not has the disease.

Event B: The test reports positive.

Event B' : The test reports negative.

2.

3.

P(A | B) = P(B | A) * P(A) / P (B)

= P(B | A) * P(A)  / [P(B | A) * P(A) + P(B | A') * P(A')]

= 0.98 * 0.0005 / [0.98 * 0.0005 + 0.05 * 0.9995]

= 0.00049 / 0.00049 + 0.049975

= 0.00049 / 0.050465

= 0.0097

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