Video: Using a Tree Diagram to Write the Subset of the Sample Space Representing an Event

Upon flipping a coin three consecutive times, use a tree diagram to determine the event 𝐴 that includes all of the outcomes where, at most, two tails are flipped.

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Video Transcript

Upon flipping a coin three consecutive times, use a tree diagram to determine the event 𝐴 that includes all of the outcomes where at most two tails are flipped.

So after flipping a coin one time, we can either land on heads or tails. If we had landed on heads on our second flip, we would now have the option of heads or tails. Or if we had landed on tails on the first flip, on our second flip, we would have an option of heads or tails. And then on the third flip, we have even more options. So in order to read a tree diagram, essentially we follow the branches from the top to the bottom.

Here’s an example. On the first flip, we could land on heads. The second flip would be on heads. And then the third flip would be on tails. So we’re interested in event 𝐴. And it includes all of the outcomes where at most two tails are flipped. So this would include the outcomes that have zero tails, one tail, or two tails.

We just can’t have three tails. So let’s go through each branch. So event 𝐴 will include heads heads heads because it has zero tails. It will also include heads heads tails because it has one tail. Heads tails heads will also be included because it has one tail and also heads tails tails because it has two tails.

Now we’re looking at the outcomes as if we had landed on tails on our first flip. And tails heads heads will be included because it has one tail. Tails heads tails is included because it has two tails. And tails tails heads is included because it has two tails. And this will be it for event 𝐴 because tails tails tails has three tails. And that is not at most two tails. That’s more than that. Therefore, these outcomes will be event 𝐴.

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