Question

Part – B:                                                                                                                                                                  

A firm purchases a microchip used in the manufacturing of LED screens from four different suppliers. TechZone supplies 30 percent of the total microchips, Advance Electronics 25 percent, PSP importers 18 percent, and TechParts inc. 32 percent. TechZone tends to have the best quality, as only 3 percent of its microchips arrive defective. Advance Electronics chips are 4 percent defective, PSP importers chips are 7 percent defective, and Parts Inc. are 6.5 percent defective.

1. If a random chip is selected, what is the probability that the chip is defective
2. A defective chip was discovered in the latest shipment. What is the probability that it came from TechZone supplies?
3. A defective chip was discovered in the latest shipment. What is the probability that it came from Parts Inc.?

Part – C:                                                                                                                                                                  

Pakistan Cricket Board in its central contract places its International players in four different categories, Category A, Category B, Category C and Emerging Players’ Category. Batsmen who are going to play in upcoming series fall into these four categories in the proportions 30 percent, 40 percent, 20 percent and 10 percent. The probability that a Category A player will get out without scoring a single run is 0.01, for Category B player its 0.04, for Category C player its 0.12 and the probability that an emerging player will get out on Zero is 0.06.

During a match after the fall of second wicket captain sent Muhammad Rizwan on batting and he got out on Zero. What is trhe probability that Muhammad Rizwan is;

1. In Category A
2. In Category B
3. In Category C

Part – D:                                                                                                                                                                  

At a University, the faculty members were surveyed and classified according to Designation and number of research publications during the last Academic year. The data are shown in the Table 6.

RESEARCH PUBLICATIONS	PROFESSOR	ASSOCIATE PROFESSOR	ASSISTANT PROFESSOR	LECTURER
0-2	3	6	16	28
3-5	2	4	12	8
MORE THAN 5	1	1	4	1

If a faculty member is selected at random, find the probability that

1. The faculty member have 3 publilcations during last year given that he/she is an Assistant Professor
2. The faculty member is Lecturer given that he/she do not have any publication.

Answer 1

B)

P(defective) = P(Tech Zone) * P(defective| Tech Zone) + P(Advance Electronics) *P(defective| Advance Electronics) + P( PSP)*P(defective| PSP) + P(tech Parts)*P(defective | techparts) =                                    0.3*0.03+0.25*0.04+0.18*0.07+0.32*0.065=   0.0524

A defective chip was discovered in the latest shipment. probability that it came from TechZone supplies =0.3*0.03/0.0524 = 0.1718

A defective chip was discovered in the latest shipment. probability that it came from Parts Inc.=0.32*0.065/0.0524 = 0.3969