Question

In a random sample of NU students, 60% of the students are Chemical engineering majors, 30% Process engineering majors, and 10% are civil majors. Of the Chemical engineering majors, 50% were females; whereas, 30% of Process engineering majors were females. Finally, 20% of the civil majors were female. Given that a person is female, what is the probability that she is a Chemical engineering major?

Answer 1

Solution:

Let us define some events as follows:

E_{​​​​​​1} : A student is chemical engineering major

E_{​​​​​2} : A student is process engineering major

E_{​​​​​3} : A student is civil major

A : A student is female

Now we have following informations :

P(E_{​​​​​​1}) = 0.60, P(E_{​​​​​​2}) = 0.30, P(E_{​​​​​​3}) = 0.10

P(A | E_{​​​​​​1}) = 0.50,  P(A | E_{​​​​​2}) = 0.30 and  P(A | E_{​​​​​3}) = 0.20

We have to obtain P(E_{​​​​​1} | A).

Using Bayes theorem, P(E_{​​​​​1} | A) is given as follows:

Given that a person is female, then the probability that she is a Chemical engineering major is 0.7317.

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