### 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.