How Does Faulty Item Compensation Affect Wholesaler Profit?

[MichaelShane]

Quesiton: A wholesalers buys items at £25 each. The wholesalers sells this in batches of 8 to retailers at £36 per item. It is know that, on average , 25 items in a thousand are faulty.

(A) Construct the probability distribution table for the number of faulty items in a batch of 8 items. All probability values must be rounded off to 5 decimal places.

(B) For any faulty item in a batch the wholesaler promises to give 2 extra items, free of further charge, to the retailer who then accepts full responsibility for the batch.
Extend your table of part (A) to indicate the wholesalers profit for each possible value of the number of faulty items in a batch of 8. Extend your table further to calculate the wholesalers expected profit on a batch of 8 items.

Kindly help me in solving the above probability problems, help will be highly appreciated.

Thank you very much in advance.

 

[ssd]

It is not an advance question of probability. Are you familier with univariate probability distributions like binomial distribution? Please show your attempt of solution to get further help.

 

[tacman]

(A) Probability distribution table for number of faulty items in a batch of 8 items:

| Number of Faulty Items | Probability |
|------------------------|-------------|
| 0 | 0.9728 |
| 1 | 0.0256 |
| 2 | 0.0016 |
| 3 | 0.0001 |
| 4 | 0 |
| 5 | 0 |
| 6 | 0 |
| 7 | 0 |
| 8 | 0 |

(B) Table showing wholesaler profit for each possible value of faulty items in a batch of 8:

| Number of Faulty Items | Wholesaler Profit |
|------------------------|--------------------|
| 0 | £88 |
| 1 | £62 |
| 2 | £36 |
| 3 | £10 |
| 4 | £-16 |
| 5 | £-42 |
| 6 | £-68 |
| 7 | £-94 |
| 8 | £-120 |

To calculate the expected profit, we need to multiply the profit for each possible value of faulty items by its corresponding probability and then add them all together.

Expected profit = (0.9728 x £88) + (0.0256 x £62) + (0.0016 x £36) + (0.0001 x £10) + (0 x £-16) + (0 x £-42) + (0 x £-68) + (0 x £-94) + (0 x £-120)

= £85.856

Therefore, the expected profit for a batch of 8 items is £85.856.