forty-five percent of the students in a dorm are business majors and fifty-five percent are non-business majors. business majors are twice as likely to do their studying at the library as non-business majors are. half of the business majors study at the library. if a randomly slected student from the dorm studies at the library, what is the probability the student is a business major

Solution :

Defining the following events as :

B : Being a Business major

α : Studying at the library

∴ Given that :

         = 0.45

Again, P [ Studying at the library | Being a Business major ] = 2 P [ Studying at the library | Being a non business major ]

  .......(1)

Again,

From (1), we get

              = 0.25

Therefore, we need,

= P[  The students is a Business major | The student studies at the library ]

By Bayes theorem

= 0.6207

c

step-by-step explanation: