Question

Three machines E₁, E₂, E₃ in a certain factory produce 50%, 25% and 25%, respectively, of the total daily output of electric tubes. It is known that 4% of the tubes produced one each of machines E₁ and E₂ are defective, and that 5% of those produced on E₃ are defective. If one tube is picked up at random from a day’s production, calculate the probability that it is defective.

Answer 1

Let D be the event that the picked up tube is defective.

Let A₁ , A₂ and A₃ be the events that the tube is produced on machines E₁ , E₂ and E₃, respectively .