Question

# At a certain college, 53% of the students are female, and 17% of the students major...

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.

 (a)What is the probability that a randomly selected female student majors in civil engineering? Round your answer to the nearest hundredth. (b)What is the probability that a randomly selected civil engineering major is female? Round your answer to the nearest hundredth.

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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