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Understanding Probability: A Step-by-Step Approach to Solving Problems

This guide provides a clear methodology for solving probability problems by determining all possible outcomes and identifying the number of favorable results. By following two essential steps—counting the possibilities and assessing which are "winners"—learners can calculate the probability as the ratio of favorable outcomes over total possibilities. The guide includes practical sample problems, ranging from single point selections to more complex scenarios, enhancing comprehension and application of probability principles. Engage in problem-solving with real-world examples to ensure a robust understanding of probability.

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Understanding Probability: A Step-by-Step Approach to Solving Problems

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  1. 1.9 Probability

  2. Two Steps for Probability Problems • Determine all possibilities in a logical manner. Count them • Determine the number of these possibilities that are “favorable”. Sometimes they are called “winners”. • Probability = (Number of Winners)/(Number of Possibilities)

  3. Sample Problems If one of the four points is picked at random, what is the probability that the point lies on the angle? Answer: Possible points = 4 Winners = 4 P/W=4/4=1=100% A B C D

  4. More Problems… If two of the four points are selected at random, what is the probability that both lie on ray CA? List all possibilities – AC, AB, AD, BC, BD, CD List winners – AC, AB, BC W/P = 3/6 = 1/2 A B C D

  5. And Again… If three of the four points are selected in a random order, what is the probability that the ordered letters will correctly name the angle shown? Answer: Done in Class 1/6 A B C D

  6. A point Q is randomly chosen on AB. What is the probability that it is within 5 units of C? Answer: Look at regions Possible Region = 12 units (15-3) Winning Region = 9 units (5 to the left and 4 to the right) W/P = 9/12 = 3/4 A C B 11 15 3

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