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A fair coin is tossed three times at random.
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Let a be the event there are at least one head.
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Let b be the event there at most two heads.
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And let c be the event there are exactly two heads.
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Let's list all of the elements of event a.
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So a is there's at least one head.
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So that means we could have a head with two tails.
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We could have a tail.
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So that can happen either one of these three ways.
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There we have one head.
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So if we have two heads, we can have this.
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And then if we want at least one, that means we could have three.
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So there is the elements of event a.
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So the probability is going to be what? well, how many of these events are there? there's going to be seven of these events.
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And when you toss a coin three times, how many events do we have? well, we have two times two times two, which is eight, so we're going to have seven out of eight.
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So now we want to know what is the events of b.
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So we want at most two heads.
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Well, at most, that means we can have one, we can have two, but we might have zeros.
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That means we could have tails, tails, and tails.
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So those events at most would be everything in green.
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So what is the probability of that happening? again, that would be seven out of eight.
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And now it says we want to know all of the events in c.
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That's where we have exactly two heads.
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So that means that's going to be here, here, and here.
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There's three items in that...