I have this question in exercise which I solved it but not sure about the answer.
There are two department in a car manufacturing company, each department is making cars. Department 1 has 10 racing cars and 30 luxury cars, while department 2 has 20 of each. A marketing manager picks a department at random, then picks a car at random. The car turns out to be a luxury car. How probable is it that the manager picked it out of department 1?
Probability of picking a luxury car from department 1 $= 1/2*(30/40)=0.375$
Probability of picking a luxury car from department 2 $= 1/2*(20/40)=0.25$
More probable than picking up from department 2.