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Video: Using Tree Diagrams to Determine the Probability of Intersection of Two Independent Events Involving Spinners

Bethani Gasparine

If two spinners are spun, where the first is numbered from 1 to 2 and the second from 1 to 9, determine the probability of both spinners stopping at even numbers using a tree diagram.

02:13

Video Transcript

If two spinners are spun, where the first is numbered from one to two and the second from one to nine, determine the probability of both spinners stopping at even numbers, using a tree diagram.

If we would spin spinner number one, we could stop at one or we could stop at two. Let’s say that we stopped at one for spinner number one. Now when we spin spinner number two, we can land on numbers from one to nine. It also could’ve happened that we would have landed on two for spinner number one. And if we had landed on two for spinner number one, then when we would spin spinner number two we would also have the opportunity to land on numbers one through nine.

So how do you read a tree diagram? Let’s look at an example. Let’s say that we would spin spinner number one and we stopped at one. And then we would spin spinner number two and we would stop at five. That means we stopped at number one for spinner number one and five for spinner number two. So these would be the possible outcomes, if we knew that we landed on one for spinner number one. These would be the possible outcomes, for- if we knew that we landed on two for spinner number one.

Tree diagrams are useful for probabilities. It helps to visualize all the different possible outcomes. Here we can see there’re 18 possible outcomes if you would spin spinner number one and then you would spin spinner number two.

So we want to find the probability of both spinners stopping at even numbers. Well, spinner number one only has one even number, that’s two. And then spinner number two would have even numbers of two, four, six, and eight. This means there are four outcomes, where we would land on even numbers for both spinners.

This means the probability of both spinners stopping at even numbers would be four out of 18.