At a certain college,
53%
of the students are female, and
17%
of the students major in civil engineering. Furthermore,
12%
of the students both are female and major in civil
engineering.

We are given here that:
P( female ) = 0.53,
P( civil engineering ) = 0.17,
Also, we are given here that:
P( female and civil engineering ) = 0.12.
a) The probability that a randomly selected female student
majors in civil engineering is computed using Bayes theorem
as:
P( civil engineering  female ) = P( female and civil engineering )
/ P(female)
= 0.12 / 0.53
= 0.23
Therefore 0.23 is the required probability here.
b) The probability that a randomly selected civil
engineering major is female is computed here using Bayes theorem
as:
P( female  civil engineering) = P( female and civil engineering )
/ P(civil engineering)
= 0.12 / 0.17
= 0.71
Therefore 0.71 is the required probability here.
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