In Exercises 21–22, a fair coin is tossed two times in succession...

Question

In Exercises 21–22, a fair coin is tossed two times in succession. The sample space of equally likely outcomes is {HH,HT,TH,TT}. Find the probability of getting two heads.

Accepted Answer

Hello. Everyone in this video, we're going to be looking at this practice problem where we want to find the probability of getting at least two heads when a fair coin is flipped three times. So in order to get started with this problem, let's think about the total number of outcomes when a coin is flipped three times total. So let's start with the outcome of a coin being flipped one time. So when a coin is flipped one time it could either be heads or tails. So there's only two total outcomes when it's flipped one time, if we increase the amount two times both flips could result in head. Both flips could result in tails. Or you could have the first flip be heads and the second flip be tails or vice versa. Where the first flip is tails and the second is heads. So you can see that by flipping the coin two times we've increased the total amount of outcomes to four. So now if we look at the coin being flipped three times you could either have all three flips result in heads Or all three flips result in tails. Or you could have the first flip be heads and the next to be tails or have tails and then heads and then tails again. Or have the first to be tails. And the last one heads Or how the first one details and the last two heads or have heads tails and then heads or have the first to be heads and the last tails. So you can see that when you have, when you flip a coin three times you could have a total of eight outcomes. Because each time that you flip a coin you could either get heads or tails. So for this problem we want the probability of getting at least two heads. So if we look at the total number of outcomes, you can see that this first one, we're all three our heads, we have at least two heads. So we can count that one you see here where we have tails and then two heads. We can count that one because that's at least two heads. We can also count this scenario where we have heads tails heads and we can also count heads heads tails. So you can see that in the total number of outcomes there's four outcomes where we have heads greater than or equal to two or the amount of heads that appear greater than or equal to two. So using this we can determine the probability of getting at least two heads. So eight is equal to the number of total outcomes and four is equal to the number of favorable outcomes because four is the number of outcomes where we have at least two heads. So in order to determine the probability of getting at least two heads, we do the number of total the number of favorable outcomes for divided by the number of total outcomes. Eight And if we simplify this, you can see this becomes one half. So one half is the probability of getting at least two heads when we flip a coin three times, and you can see that that aligns with answer choice C. So hopefully this video helped and see you next time.

In Exercises 21–22, a fair coin is tossed two times in succession. The sample space of equally likely outcomes is {HH,HT,TH,TT}. Find the probability of getting two heads.

Key Concepts

Sample Space

Probability

Equally Likely Outcomes

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