Instructor: Hello, students.
We are now going to go over problem 6A.
This is the last problem we are covering from chapter five.
I know this has been a lot, but I really do want to go
over these problems because this will help you
not only do the homework problems,
but also to do well in the test.
So problem six again states a study is conducted
to assess the impact of caffeine consumption,
smoking, alcohol consumption
and physical activity on cardiovascular disease.
Suppose that 40% of participants consume caffeine and smoke.
If eight participants are evaluated,
what is the probability that exactly four
do not consume caffeine or smoke?
So from reading the problem, I think you kind of understand
that here we are kind of doing the reverse
of what we did in part A, but it is a little different
but we still have four, we just have,
but now we are looking for four
that do not consume caffeine or smoke.
However, we have to use the same binomial distribution
and therefore, I start writing the formula again.
However, as you can see here
that the probability will change
because now there is a 40%
of the participants,
(instructor clearing throat) excuse me,
who consume caffeine or smoke.
So 60% does not.
So because of this,
we are going to be doing this a little bit differently.
Well, the probability here basically will be changing.
So here we have still x equal to four,
here the n is still eight.
That is not going to change.
So it's eight factorial, again, four factorial
eight minus four factorial.
However, this p right now will be 0.6 to the power four.
And this will be be one minus 0.6
and that will be to the power eight minus four.
So here, if you recall, we already did this part
of the calculation in part A, so I'm not going to repeat it.
So what I'm going to do is basically write this down
as two times seven times five
and then 0.6 to the power four will be again 0.1296
and this one will be 0.0256.
So when we do this multiplication all the way,
we get 0.2322, and basically that is 23.22%.
So basically, we have ended up with almost the same result.
So going back again to our problem statement,
if eight participants are evaluated,
what is the probability?
So the probability is 23.22,
exactly four that do not consume caffeine or smoke.
So that's basically the conclusion.
And I will write this one down
because we do have some space here.
So the probability is 23.22%
probability,
or if you really want to be cor,
we can say 0.2322.
Probability
that exactly
four
do not
consume caffeine or smoke.
Okay. All right.
So thank you again very much for your patience
and going with me through all these problems.
Chapter five, we have covered quite a few problems.
Again, it's very important you go through these problems,
not once, but at least a couple of times.
It'll really, really help you.
I really enjoyed solving these problems
and hopefully, you have enjoyed learning this too.
So again, please feel free to reach out
if you have any questions.
I'm here to help.