In the warm up, I knew students had a grasp on the Fundamental Counting Principle when it involved events such as choosing 4 tops and 5 pants….how many possible outfits? They knew you just multiply each events’ outcome to find the total possible outcomes. We did an example involving Amy’s ice cream (9 ice cream flavors, 31 “crush’ns” options…how many possible combos of 1 topping ice cream flavors can we make?) (9 x 31 = 279 outcomes). They got it!
However, we spent lots of time going over the sample space problems that involve more than 2 events: flipping 3 coins, or problems like, “How many outcomes are there on a three-question true or false test?”
Students inevitably want to multiply the 3 questions x 2 choices each to get 6 possible outcomes. We had to review that the Fundamental Counting Principle states that you multiply the outcomes of each event. In this case, that would mean 2 outcomes for question 1 (true/false), 2 outcomes for question 2 (true/false), and 2 outcomes for question 3(true/false). That means, we multiply 2 x 2 x 2 to get 8. This review seemed to help clarify the misconceptions.