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Business Mathematics I Homework 6 Prepared for Math 115a, Section: Instructor: Date: By Team: We, the undersigned, maintain that each of us participated fully and equally in the completion of this assignment and that the work contained herein is original. Furthermore, we acknowledge that sanctions will be imposed jointly if any part of this work is found to violate the Student Code of Conduct, the Code of Academic Integrity, or the policies and procedures established for this course. ______________________________ Name (printed) ______________________________ Signature ______________________________ Name (printed) ______________________________ Signature ______________________________ Name (printed) ______________________________ Signature ______________________________ Name (printed) ______________________________ Signature ______________________________ Name (printed) ______________________________ Signature 1. Box I contains three black balls and two white balls. Box II contains one black ball and three white balls. A person chooses one of the boxes at random, and then draws one of the balls in that box. Let I be the events that the ball is drawn from Box I, let II be the event that the ball is drawn from Box II, let B be the event that the selected ball is black, and let W be the event that the selected ball is white. Compute P ( I | W ) and P ( I | B ) . Solution. 2. Box I contains three black balls and two white balls. Box II contains one black ball and three white balls. A person chooses one of the boxes at random, and then draws one of the balls in that box. Let I be the events that the ball is drawn from Box I, let II be the event that the ball is drawn from Box II, let B be the event that the selected ball is black, and let W be the event that the selected ball is white. Compute P( II | W ) and P ( II | B) . Solution. 3. The probability that a defective part is produced by a certain machine depends on the condition of the machine. If the machine is in good condition, then the probability of a defective part is 0.02. If it is in fair condition, then the probability of a defective part is 0.10. If it is in poor condition, then the probability of a defective part is 0.3. The probability that the machine is in good condition is 0.8, the probability that it is in fair condition is 0.1, and the probability that it is in poor condition is 0.05. If a defective part is found, what is the probability that it was produced while the machine was in good condition? Solution. 4. The probability that a defective part is produced by a certain machine depends on the condition of the machine. If the machine is in good condition, then the probability of a defective part is 0.02. If it is in fair condition, then the probability of a defective part is 0.10. If it is in poor condition, then the probability of a defective part is 0.3. The probability that the machine is in good condition is 0.8, the probability that it is in fair condition is 0.1, and the probability that it is in poor condition is 0.05. If a defective part is found, what is the probability that it was produced while the machine was in poor condition? Solution.