If anyone can help. Please help me understand this.

Question

A company manufactures tires at a cost of $30 each. The following are probabilities of defective tires in a given production run: probability of no defective tires: 10%; probability of 1% defective tires: 30%; probability of 2% defective tires: 40%; probability of 3% defective tires: 20%. When a defective tire is detected, it must be removed from the assembly line and replaced. This process adds an extra $5 to the cost of the replaced tire. What is the expected cost to the company of a batch of 3000 tires?

Answer 1

The company starts with a fixed cost of $30/tire*3000 tires=$90,000. This is the base cost.

Then we calculate costs from tire failure.

If no tires fail, there is no extra cost.

If 1% of tires fail, there is an extra cost of $5/tire*0.01*3000 tires=$150

If 2% of tires fail, there is an extra cost of $5/tire*0.02*3000 tires=$300

If 3% of tires fail, there is an extra cost of $5/tire*0.03*3000 tires=$450.

Now add the costs multiplied by the probability of each failure level.

$0*0.1+$150*0.3+$300*0.4+$450*0.2=$0+$50+$120+$90=$260. This is the expected cost from failure.

Now add base cost to expected cost from failure to give an expected total cost of $90,260.