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MER301 Probability Problems and Team Exercise for Engineering Reliability

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5 diapositives · 191 Views · Aug 16, 2014

This document presents a series of probability problems suitable for MER301 Engineering Reliability class. It includes fundamental concepts such as mutually exclusive events and calculating probabilities with dice and cards. The problems engage students in practical applications like assessing surgical treatment success rates based on exercise frequency, and challenges them to compare probabilities of different outcomes. Additionally, it contains a team exercise focusing on critical measures of product quality (CTQs) for engineered products like toaster ovens and jet engines, emphasizing the statistical nature of engineering.

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  1. MER301 –Probability Problems -LECTURE 1: Basic Probability Theory Homework -CTQ Team Exercise Assignment MER301: Engineering Reliability Lecture 16

  2. Probability Problems(page 1) Problem 1(1 pt) Two events are mutually exclusive. If P(A)=0.6 and P(B)=0.4, what is and Problem 2 (1 pt) A) What is the probability of rolling a 5 in one roll of a single die? B) What is the probability of rolling a 5 in one roll of a single die if you know that the result is an odd number? Problem 3(2 pts) A) In a family with three children, what is the probability that all are girls? B) If you know that at least one of the children is a girl, what is the probability that all are girls? C) If you know the eldest is a girl, what is the probability that all are girls? Problem 4(1 pts) If you toss a coin five times, what is the probability that the first three tosses are tails or the last three tosses are heads? MER301: Engineering Reliability Lecture 1 2

  3. Probability Problems(page 2) Problem 5(1 pt) What is the probability of picking two kings from a deck of cards in two draws IF the first card is replaced before the second draw What is the probability of picking two kings from a deck of cards in two draws IF the first card is not replaced before the second draw Problem 6(2 pts) A hundred people undergo surgical treatment for spinal issues. Sixty of them show improvement. Of the sixty, forty-five exercise regularly (at least 3 times/week). Five of those who did not show improvement also exercise regularly. A)What is the probability that the treatment is successful, given that the person exercised. B)What is the probability that the treatment is successful, given that the person did not exercise MER301: Engineering Reliability Lecture 1 3

  4. Probability Problems(page 3) • Problem 7(2 pts) • Is the probability of rolling a six in four rolls of a single dice greater than, the same as, or less than the probability of rolling a pair of sixes in twenty-four rolls of a pair of dice? What are the probabilities of each?

  5. CTQ Team Exercise For two common engineered products, a toaster oven and a jet engine,give examples of each of the following Critical Measures of Product Quality (CTQ’s) Performance Cost Reliability Operational Flexibility Variation that must be considered in the design Discuss why engineering is inherently statistical in nature Give examples of significant variations in the toaster oven and the jet engine, such as critical hardware dimensions or functional characteristics Give examples of Sampling that you have encountered The needle problem…what is it? Conduct a 30 sample trial and report the results… MER301: Engineering Reliability CTQ Team Exercise 5