Question

Excell Computers promptly shipped two servers to its biggest client. The company profits RM5,000 on each one of these big systems. The shipping worker randomly selected the system without replacement that were delivered from 15 computers in stock. The system contain 4 refurbished computer, with 11 new computers in the warehouse.

If the client gets two new computers, Excell earns RM10,000 profit. If the client gets a refurbished computer, it’s coming back for replacement and Excell must pay the RM400 shipping fee, with leaves RM9,600 profit. If both computers shipped are refurbished, consequently the client will return both and cancel the order. As a result, Excell will be out any profit and left with RM8,000 in shipping cost. Let X be a random variable for the amount of the profit earned on the order.

a. Illustrate the event.                                                

b. Construct a probability distribution table and the amount of profit earned for the computer condition.

c. Calculate the expected profit then interpret the value.    

Answer 1

I assume, the shipping cost is RM400 for each computer and the correct statement in the question would be As a result, Excell will be out any profit and loss of RM800 in shipping cost.

a.

The events are,

X = RM10,000 No shipped computers were refurbished.

X = RM9,600 One of the shipped computers was refurbished.

X = -RM800 Both shipped computers were refurbished.

b.

P(X = RM10,000) = Probability that 1st computer is not refurbished * Probability that 2nd computer is not refurbished = (11/15) * (10/14) = 0.5238095

P(X = RM9,600) = Probability that 1st computer is not refurbished * Probability that 2nd computer is refurbished + Probability that 1st computer is refurbished * Probability that 2nd computer is not refurbished = 11/15) * (4/14) + (4/15) * (11/14) = 0.4190476

P(X = -RM800) = Probability that 1st computer is refurbished * Probability that 2nd computer is refurbished = (4/15) * (3/14) = 0.05714286

The probability distribution table and the amount of profit earned for the computer condition is,

X	P(X)
RM10,000	0.5238095
RM9,600	0.4190476
-RM800	0.05714286

c.

Expected profit =

= RM10,000 * 0.5238095 + RM9,600 * 0.4190476 - RM800 * 0.05714286

= RM9,215.24

Interpretation - In the long run, the expected profit of Excell Computers is RM9,215.24 per order of two computers.