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 tube produced on 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 A be the event that the picked up tube is defective.

Let A₁, A₂, A₃ be events such that

A₁ = event of producing tube by machine E₁

A₂ = event of producing tube by machine E₂

A₃ = event of producing tube by machine E₃