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Understanding Basic Probability Through Simple Steps

Mastering the fundamentals of probability is essential for solving problems effectively. This guide outlines a logical two-step approach: first, determine all possible outcomes, and second, count the number of favorable outcomes, often referred to as "winners." The probability is then calculated by dividing the number of winners by the total number of possibilities. The document provides examples to illustrate this method, including practical problems involving random selections and the calculation of probabilities within geometrical contexts.

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Understanding Basic Probability Through Simple Steps

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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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