Video: Determining the Probability of Intersection of Two Independent Events Involving Spinners

Two spinners are spun. The first spinner is numbered from 1 to 7, and the second spinner is numbered from 1 to 8. Using a tree diagram, determine the probability of both spins being the same number.

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Video Transcript

Two spinners are spun. The first spinner is numbered one to seven. And the second spinner is numbered from one to eight. Using a tree diagram, determine the probability of both spins being the same number.

Once the first spinner has been spun, there are seven options to land on numbers one through seven. And now for the second spin, there are eight options. So the blue represents spin number one. And then the pink option represents spin number two.

So, for example, for our first spin, we landed on number one. And for the second spin, we also landed on number one. And this is actually the probability that we’re looking for, the probability of both spins being the same number.

So here’s one place that that could happen. Here’s a second, a third place this could happen, and a fourth, fifth, sixth, and seventh place that can happen. So there are seven opportunities where this could happen.

Now what do we put it out of? How many different options were there? We could have landed on one and then two or one and then three, one and then four, and so on. So if we landed on one for the first spinner, there would be eight options for that for the second spin. So there are eight possibilities here and here and here, here, and these places too.

So altogether, how many possibilities are there? 56. So if we would spin spinner number one and then spin spinner number two, there are 56 different possibilities that we could have. And out of the 56, the probability of both spins being the same number would be seven out of the 56.

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