2.2 The Fundamental Counting Principle

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2.2 The Fundamental Counting Principle

Learning Goal I am learning to use the fundamental counting principle for counting and to solve problems Investigate Determining the Number of Outcomes 1 2 a) Roll one die and flip a coin. Make a list or a diagram to illustrate all the possible outcomes. b) How many outcomes are possible? Roll one die, flip a coin, and spin a spinner with four equal sections. Without making a list or diagram, determine how many outcomes are possible. Describe your method. 3 Randomly select a number between 1 and 100, and a letter from the alphabet. How many outcomes are possible? How did you know this without counting all the outcomes? 4 Events A and B are independent. Event A has 𝑚 outcomes. Event B has 𝑛 outcomes. How many outcomes are possible, in total, if both events occur together? 5 Explain why your method in step 4 works. Fundamental Counting Principle If one event can occur in 𝑚 ways and a second event can occur in 𝑛 ways, 𝑚 × 𝑛 ways.

Example 1 Counting Repeated Independent Trials You flip a fair coin. How many outcomes are possible with a) b) two flips? three flips? Example 2 Counting Repeated Trials Without Replacement Two letter tiles are chosen from full alphabet without replacement. How many possible outcomes are there? Reflect R1. Evan reasons that when rolling two 10-sided dice, since each has 10 outcome, there are 10 + 10 = 20 outcomes in total. Is he right or wrong? Explain. R2. If a tree diagram has 3 levels with 𝑝 outcomes at the first level, 𝑞 outcomes at the second level and 𝑟 outcomes at the third level, how many outcomes are there in total? Homework p. 73 #1 – 10, 13 – 16

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