1. 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;

a) In Category A b) In Category B c) In Category C

2.In a Internee program at Airline Company, 60 percent of the internees are female and 40 percent male. 80 percent of the females are business students, and 65 percent of the males are business students. a) An internee is selected at random. What is the probability that the person selected is a female who is not a business student? b) Are gender and field of study, independent in this case? Why?

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