Question

A medical study attempted to identify risk factors for severely premature births. A large sample of expectant mothers received a health assessment and was then classified as “low risk,” “moderate risk” and “high risk” for premature birth.

Let LOW denote the event in which an expectant mother is assessed as having a low risk of premature birth.

Let MOD denote the event in which an expectant mother is assessed as having a moderate risk of premature birth.

Let HIGH denote the event in which an expectant mother is assessed as having a high risk of premature birth.

Let PRE denote the event in which a mother gives birth to a premature baby.

Let TERM denote the event in which a mother carries a baby to full term and does not experience a premature birth.

The study offered the following conditional probabilities:

Pr(LOW | PRE) = .10 Pr(LOW | TERM) = .75

Pr(MOD | PRE) = .20 Pr(MOD | TERM) = .15

Pr(HIGH| PRE) = .70 Pr(HIGH| TERM) = .10

In the overall sample, 3% of babies were born prematurely. So you have a prior belief that Pr(PRE) = .03.

a) An expectant mother is assessed as having a high risk of premature birth. Conditional on this assessment, what is the probability that she will experience a premature birth?

Answer 1

Note that:

Since, Pr(PRE) = 0.03

=> Pr(TERM) = Pr(carrying a baby to full term)

= 1 - Pr(giving birth to a premature baby)

= 1 - Pr(PRE)

= 1 - 0.03

= 0.97

a)

Now, we are given that an expectant mother is assessed as having a high risk of premature birth, conditional on this the probability that she will experience a premature birth is given by:

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