Question Video: Determining the Probability of Compound Events Involving Spinners Mathematics

What is the probability of the pointer landing on an even number when the given spinner is spun?

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Video Transcript

What is the probability of the pointer landing on an even number when the given spinner is spun?

When we have a question like this, we can assume that the spinner is fair. And by that we mean it’s not biased or weighted, for example, so that the pointer will land more frequently on one section than another. We can see that all the sections are the same size. In particular, the angle made at the center of this spinner in each sector will be the same.

Because there will just be one outcome any time the spinner is spun, then we can use a key probability formula. The probability of an event is equal to the number of possible outcomes over the total number of outcomes. So what event are we interested in here? Well, it’s the probability of the pointer landing on an even number. And we can write this as P and even in parentheses. Then the number of possible outcomes is the number of even values on the spinner. And the total number of outcomes is the total number of values on the spinner.

So let’s work out the even and the odd values on the spinner. Well, just 12 and 14 are even, so that’s two even values. And then there’s eight different values on the spinner. Notice that we’ve also included the even numbers as they’re still part of the total number of values. Two over eight simplifies to one-quarter. So the answer is that the probability of the pointer on this spinner landing on an even number is one-quarter.

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