Question Video: Applications of the Counting Principle (Product Rule)

Two spinners are spun. The first spinner is numbered from 1 to 5, and the second spinner is numbered from 1 to 7. Determine the total number of possible outcomes.

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Video Transcript

Two spinners are spun. The first spinner is numbered from one to five, and the second spinner is numbered from one to seven. Determine the total number of possible outcomes.

To answer this question, weโ€™re going to recall the fundamental counting principle. This says that if A and B are independent events, that is, the outcome of one does not affect the outcome of the other and if A has ๐‘š possible outcomes and B has ๐‘› possible outcomes, the total number of possible outcomes of the two events together is ๐‘š times ๐‘›; itโ€™s the product of these.

Now, our two events are spinning the first spinner and spinning the second spinner. And so, we need to consider the total number of outcomes for each event. The first spinner is numbered from one to five, so there are five different scores that we can receive when we spin that first spinner. Then the second spinner is numbered from one to seven. So, there are seven different outcomes; there are seven different scores that we could get. The product rule for counting or the counting principle says that the total number of possible outcomes is the product of these two numbers. Itโ€™s five times seven and of course that is equal to 35. And this means that when we spin these two spinners, we can get a total number of 35 possible outcomes.

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