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<v Instructor>Hello, students.</v>

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We are now going to go over problem 6A.

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This is the last problem we are covering from chapter five.

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I know this has been a lot, but I really do want to go

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over these problems because this will help you

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not only do the homework problems,

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but also to do well in the test.

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So problem six again states a study is conducted

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to assess the impact of caffeine consumption,

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smoking, alcohol consumption

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and physical activity on cardiovascular disease.

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Suppose that 40% of participants consume caffeine and smoke.

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If eight participants are evaluated,

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what is the probability that exactly four

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do not consume caffeine or smoke?

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So from reading the problem, I think you kind of understand

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that here we are kind of doing the reverse

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of what we did in part A, but it is a little different

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but we still have four, we just have,

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but now we are looking for four

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that do not consume caffeine or smoke.

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However, we have to use the same binomial distribution

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and therefore, I start writing the formula again.

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However, as you can see here

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that the probability will change

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because now there is a 40%

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of the participants,

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(instructor clearing throat)
excuse me,

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who consume caffeine or smoke.

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So 60% does not.

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So because of this,

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we are going to be doing this a little bit differently.

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Well, the probability here basically will be changing.

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So here we have still x equal to four,

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here the n is still eight.

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That is not going to change.

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So it's eight factorial, again, four factorial

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eight minus four factorial.

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However, this p right now will be 0.6 to the power four.

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And this will be be one minus 0.6

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and that will be to the power eight minus four.

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So here, if you recall, we already did this part

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of the calculation in part A, so I'm not going to repeat it.

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So what I'm going to do is basically write this down

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as two times seven times five

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and then 0.6 to the power four will be again 0.1296

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and this one will be 0.0256.

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So when we do this multiplication all the way,

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we get 0.2322, and basically that is 23.22%.

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So basically, we have ended up with almost the same result.

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So going back again to our problem statement,

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if eight participants are evaluated,

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what is the probability?

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So the probability is 23.22,

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exactly four that do not consume caffeine or smoke.

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So that's basically the conclusion.

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And I will write this one down

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because we do have some space here.

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So the probability is 23.22%

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probability,

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or if you really want to be cor,

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we can say 0.2322.

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Probability

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that exactly

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four

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do not

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consume caffeine or smoke.

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Okay. All right.

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So thank you again very much for your patience

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and going with me through all these problems.

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Chapter five, we have covered quite a few problems.

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Again, it's very important you go through these problems,

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not once, but at least a couple of times.

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It'll really, really help you.

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I really enjoyed solving these problems

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and hopefully, you have enjoyed learning this too.

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So again, please feel free to reach out

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if you have any questions.

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I'm here to help.