A company manufactures tires at a cost of $60 each.

Question

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

As I read this all defective tires, whether 1%, 2%, or 3%, add a cost of $5.

Note that all of these words say the the probability of a defect is 90%.

 

The estimated additional cost is 5(9/10), or 4.50 per tire

 

The expected cost for a batch of 3000 would be 3000(4.5), or 13500.

 

$13,500.

Answer 2

Hello Ivy,

 

This is an expected value problem similar to several others you've asked about before.

 

With a batch of 3000 tires, you can list the number of defective tires and the probability of each.

 

0%(3000) = 0 defective; probability 0.10

1%(3000) = 30 defective; probability 0.30

2%(3000) = 60 defective; probability 0.40

3%(3000) = 90 defective; probability 0.20

 

The expected number of defective tires is

0*0.10 + 30*0.30 + 60*0.40 + 90*0.20

 

Multiply this by $5/defective tire, and you get the expected cost.