Question

Three machines E_1, E₂ and E₃ in a certain factory producing electric bulbs, produce 50%, 25% and 25% respectively, of the total daily output of electric bulbs. It is known that 4% of the bulbs produced by each of machines E₁ and E₂ are defective and that 5% of those produced by machine E₃ are defective. If one bulb is picked up at random from a day's production, calculate the probability that it is defective.

Answer 1

Let  A₁ : Event that the bulb is produced by machine E₁

A₂ : Event that the bulb is produced by machine E₂

A₃ : Event that the bulb is produced by machine E₃

A : Event that the picked up bulb is defective

 Here,   P(A₁) = 50% = 50/100 = 1/2,

.'. The probability that the picked bulb is defective,