Three machinesE1, 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 E3are defective. If one bulb is picked up at random from a day’s production, calculate the probability that it is defective.

Explanation

To solve the problem, we need to calculate the probability that a randomly picked bulb from the factory is defective. We will use the law of total probability. Let's break down the solution step by step.

### Step 1: Define the Events
Let:
- \( A_1 \): Event that the bulb is produced by machine \( E_1 \)
- \( A_2 \): Event that the bulb is produced by machine \( E_2 \)
- \( A_3 \): Event that the bulb is produced by machine \( E_3 \)
- \( A \): Event that the bulb is defective
...