Question

Using game simulation to teach a course. In Engineering Management Research (May 2012), a simulation game approach was proposed to teach concepts in a course on production. The proposed game simulation was for cola or television production. The products are two color television models, A and B. Each model comes in two colors, red and black. Also, the quantity ordered for each model can be 1, 2, or 3 televisions. The choice of model, color, and quantity is specified on a purchase order card.

a. Using a tree diagram, list how many different purchase order cards are possible. (These are the sample points for the experiment.)

b. Suppose, from past history, that black color TVs are in higher demand than red TVs. For planning purposes, should the engineer managing the production process assign equal probabilities to the simple events, part a? Why or why not?

Short answer

1. 12 sample points. The sample points are AR1, AR2, AR3, ABL1, ABL2, ABL3, BR1, BR2, BR3, BBL1, BBL2, and BBL3.
2. NO, the probability to the sample point that was determined in part a should not be equal.

Step-by-step solution

Important formula

The formula for probability is$\mathbf{P}\mathbf{=}\frac{\mathrm{favourable}\mathrm{outcomes}}{\mathrm{total}\mathrm{outcomes}}$

Draw a tree diagram.

Here given: The products are two colors television models, A and B. Each model comes in two colors, red(R) and black(BA).Thequantity ordered for each model can be 1, 2, or 3 televisions.

The tree diagram is

Hence, the sample points are

AR1, AR2, AR3, ABL1, ABL2, ABL3, BR1, BR2, BR3, BBL1, BBL2, BBL3.

what is the result if the probability to the sample point that was determined in part a should be equal.

NO, the probability to the sample point that was determined in part a should not be equal because if the engineer assigns similar probabilities to black and red TVs then there will be a shortage of black TVs. Since the demand for them was higher, and a surplus of red TVs.

Therefore, NO, the probability to the sample point that was determined in part a should not be equal.