Video: Writing the Subset of a Sample Space Representing an Event upon Flipping a Coin

A coin is flipped three consecutive times. Which of the following represents the event of getting heads on the first flip? [A] 𝐴 = {(H, H, H), (H, H, T), (H, T, H)} [B] 𝐴 = {(H, H, H), (H, H, T), (H, T, H), (H, T, T)} [C] 𝐴 = {(H, H, H)} [D] 𝐴 = {(T, H, H), (T, H, T), (T, T, H), (T, T, T)}.

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Video Transcript

A coin is flipped three consecutive times. Which of the following represents the event of getting heads on the first flip?

Here are our four answer choices. First, we’re going to create a tree diagram to represent our coin being flipped three consecutive times. If we flip a coin one time, there are two different outcomes we will have: heads or tails.

From here, we need to create a second flip. We would have heads or tails from our first branch. We would also have heads and tails from our second branch. When we read our question carefully though, we see that we’re only interested in the times when heads happened on the first flip. This means we’re no longer interested in what happens on this top branch. We can disregard it.

And then we can focus on our third flip. From the heads-tail branch, we’ll have another heads and another tails. From the heads- heads branch, we’ll have the outcome of heads and tails.

Now, we need to record the sequence of each branch. First, we have heads, tails, heads, which we can write like this. From there will have heads, tails, tails written like this: H, T, T; on our next branch, heads, heads, heads, written H, H, H; our last branch sequence heads, heads, tails: H, H, T. These are the four cases we would have that represents flipping coins three times and getting an H as the first coin flip.

We can take this information, compare it to our four answer choices, and see which one is correct. Answer choice C only has one sequence. We know that that can’t be true. If we look closely at answer choice D, it’s all the cases when a tails happened on the first flip. This is not going to help us. Answer choice A and answer choice B are very similar. However, answer choice A is missing one of the cases. It only list three cases. We know that it can’t be answer choice A. Answer choice B represents the four cases in an event of getting heads on the first flip.

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