A common blood test performed on pregnant women to screen for chromosome abnormalities in the fetus measures the human chorionic gonadotropin (hCG) hormone. Suppose that in a given population, 4% of fetuses have a chromosome abnormality. The test correctly produces a positive result for a fetus with a chromosome abnormality 90% of the time and correctly produces a negative result for a fetus without an abnormality 85% of the time.
(a) What proportion of women who are tested get a negative test result? Write a probability statement and find the answer.
(b) What proportion of women who get a positive test result are actually carrying a fetus with a chromosome abnormality? Write a probability statement and find the answer.

(a) The proportion of women who are tested, get a negative test result is 0.82.

(b) The proportion of women who get a positive test result are actually carrying a fetus with a chromosome abnormality is 0.20.

Step-by-step explanation:

The Bayes' theorem states that the conditional probability of an event E, of the sample space S, given that another event A has already occurred is:

The law of total probability states that, if events E₁, E₂, E₃... are parts of a sample space then for any event A,

Denote the events as follows:

X = fetus have a chromosome abnormality.

Y = the test is positive

The information provided is:

Using the above the probabilities compute the remaining values as follows:

(a)

Compute the probability of women who are tested negative as follows:

Use the law of total probability:

Thus, the proportion of women who are tested, get a negative test result is 0.82.

(b)

Compute the value of P (X|Y) as follows:

Use the Bayes' theorem:

Thus, the proportion of women who get a positive test result are actually carrying a fetus with a chromosome abnormality is 0.20.

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step-by-step explanation:

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step-by-step explanation: