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

Solution

Back-up Theory

Number of ways of selecting r things out of n things is given by ⁿC_r = (n!)/{(r!)(n - r)!}……(1)

Values of ⁿC_r can be directly obtained using Excel Function: Math & Trig COMBIN……. (1a)

Probability of an event E, denoted by P(E) = n/N ………………………………………………(3)

where

n = n(E) = Number of outcomes/cases/possibilities favourable to the event E and

N = n(S) = Total number all possible outcomes/cases/possibilities.

If a discrete random variable, X, has probability function, p(x), x = x1, x2, …., xn, then

Expected value = Mean (average) of X = E(X) = µ = Σ{x.p(x)} summed over all possible values of x.. (4)

Now to work out the solution,

Part (a)

The events are:

Event 1: The client gets two new computers

Event 2: The client gets two refurbished computers

Event 3: The client gets one new and one refurbished computers

Answer 1

Part (b)

Event 1:

The client gets two new computers

There are in total 15 computers out of which 11 are new. So, vide (1), number of ways of

the client getting two new computers = ¹¹C₂ = 55. Vide (3), this forms n = 55.

Number of ways 2 out of 15 computers can be sent ¹⁵C₂ = 105. Vide (3), this forms N = 105.

So, vide (3) again, P(The client gets two new computers) = 55/105 = 11/21 = 0.5238 ...... (5)

Since each new computer fetches a profit of 10000, total profit = 20000 ............................(6)

Event 2

The client gets two refurbished computers:

There are in total 15 computers out of which 4 are refurbished. So, vide (1), number of ways of the client getting two refurbished computers = ⁴C₂ = 6. Vide (3), this forms n = 6.

Number of ways 2 out of 15 computers can be sent ¹⁵C₂ = 105. Vide (3), this forms N = 105.

So, vide (3) again,

P(The client gets two refurbished computers) = 6/105 = 2//35 = 0.0571 ............................ (7)

Since in this case company does not make sale but incurs a shipping cost of 8000 total loss

= 8000 or a profit of – 8000..................................................................................................(8)

Event 3

The client gets one new and one refurbished computers:

There are in total 15 computers out of which 11 are new and 4 are refurbished. So, vide (1), number of ways of the client getting one new and one refurbished computer = (⁴C₁) x (¹¹C₁) = 44. Vide (3), this forms n = 44.

Number of ways 2 out of 15 computers can be sent ¹⁵C₂ = 105. Vide (3), this forms N = 105.

So, vide (3) again,

P(The client gets one new and one refurbished computers) = 44/105 = 0.4190 ................ (9)

In this case company makes a profit of 10000 on one and – 8000 on the other or a net profit of 2000 .................................................................................................................................(10)

To summarise,

Event	Probability	Profit
The client gets two new computers	0.5238	20000
The client gets two refurbished computers	0.0571	- 8000
The client gets one new and one refurbished computers	0.4190	2000

[Note that total probability is 1]

Answer 2

Part (c)

Vide (4), second and third columns of the above table, the expected profit

= RM10857.2 Answer 3

DONE