Make an Organized List and Simulate a Problem

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Presentation transcript:

Make an Organized List and Simulate a Problem COURSE 2 LESSON 12-3 Two questions on a multiple-choice test each have five answer choices. What is the probability of guessing on both questions and answering only one correctly? Your goal is to find the probability of guessing the correct answer to one of the two questions and guessing the wrong answer to the other one. 12-3

Make an Organized List and Simulate a Problem COURSE 2 LESSON 12-3 (continued) Method 1 Make an organized list Make an organized list to find the total number of possible outcomes and the number of favorable outcomes. AA BA CA DA EA AB BB CB DB EB AC BC CC DC EC AD BD CD DD ED AE BE CE DE EE 12-3

Make an Organized List and Simulate a Problem COURSE 2 LESSON 12-3 (continued) There are a total of 25 possible outcomes. Assume that the correct answers are AA. Of the 25 outcomes, 8 include a single correct answer. So the theoretical probability of guessing one and only one correct answer is , or 0.32. 8 25 12-3

Make an Organized List and Simulate a Problem COURSE 2 LESSON 12-3 (continued) Method 2 Simulate the problem To simulate a problem, first design a model. Each question has 5 equally likely answers. Using a spinner with 5 equal parts makes sense since it has 5 equally likely outcomes. Spin the pointer 100 times and divide the results into groups of 2. You now have 50 pairs of answers. ED EE AA DA DE BC BD AA CB BB BC BA BA DB BA CB CB BB AE DB CC CB EA AD BC AA DA CC BC DB ED DB BB BD CA CB AC BD EE EA BD CD EA DA EA ED AB AA CB DB 12-3

Make an Organized List and Simulate a Problem COURSE 2 LESSON 12-3 (continued) Now you can find the experimental probability. Note that 15 pairs contain a single A. P(guess one of two questions correctly) = = 0.3 number of times an event occurs total number of trials 15 50 = The experimental probability of guessing only one of the answers correctly is 0.3. 12-3

Make an Organized List and Simulate a Problem COURSE 2 LESSON 12-3 (continued) In Method 1, you found the theoretical probability. In Method 2, you found one value for the experimental probability, which is slightly less than the theoretical probability. Repeating the simulation may result in a different experimental probability. The more trials you conduct, the more likely it is that the experimental probability will be close to the theoretical probability. 12-3

Make an Organized List and Simulate a Problem COURSE 2 LESSON 12-3 Solve the problem by either making an organized list or simulating the problem. A dog will have a litter of three puppies. The probabilities of males and females are equal. What is the probability that there will be 3 males in the litter? 1 8 12-3