Question

1. The department has a study room and a game room available for students. At any point in time, the probability the study room is being used by at least one student is 0.90 and the probability the game room is being used by at least one student is 0.50. At any point in time, given that the game room is being used by at least one student, the probability the study room is being used is 0.75. a) Are the events that the study room is being used and the game room is being used independent? b) Find the probability that at some point in time, both rooms are in use. 2. In a certain supermarket, three suppliers (S1, S2, and Si) supply 50%, 35%, and 15% of a product, respectively. It is known from past experience that 0.5%, 1%, and 2% of the products provided by each supplier, respectively, are defective. Now, suppose that a customer randomly buys a product. What is the probability that it is defective? a) b) Given that a product is found to be defective, what is the probability it was supplied by supplier S3?

Answer 1