Question 1200654
.
The prevalence of smoking among youth in a certain country is 18%. 
Suppose we select six individuals from the youth
What is the probability that at least one is a smoker?
~~~~~~~~~~~~~~~~~



For this and many other similar problems, there is another way to solve,
which is much shorter and requires less calculations (and even less knowledge).



<pre>
The problem asks about "at least one person".


    +------------------------------------------------------+
    |  In such cases, the complement is "no one person",   |
    |      so let's calculate the probability that         | 
    |         NO ONE of 6 individuals is a smoker.         |
    +------------------------------------------------------+


It is  P = {{{(1-0.18)^6}}} = 0.3041   (rounded).

But we need the COMPLEMENTARY probability - - - so, our answer is  

    P' = 1 - 0.3041 = 0.6960  (rounded).
</pre>

Solved.


---------------


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Thus you may know nothing about the binomial distribution;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;you may know nothing about the relevant theory and formulas - nevertheless,
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;your intuition and your common sense will lead you to the right answer.



To see many other similar &nbsp;(and different) &nbsp;solved problems of this type, &nbsp;look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-probability-problems-using-complementary-probability.lesson>Solving probability problems using complementary probability</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-probability-problems-using-complementary-probability-REVISITED.lesson>Solving probability problems using complementary probability REVISITED</A> 

in this site.



Every time, &nbsp;when you solve a &nbsp;Probability problem which asks about &nbsp;" at least one ",
think about the complementary event &nbsp;" No one ".


As a rule, &nbsp;it is easier to calculate, &nbsp;and it gives you an easy and straightforward 

way to get the answer. &nbsp;As a reward or a bonus, &nbsp;this way is, &nbsp;as a rule, &nbsp;more elegant.

So you earn additional scores in the eyes of other people - your friends, &nbsp;your classmates, 

your teacher, &nbsp;your potential employer at the interview, &nbsp;or your students, &nbsp;if you are a teacher.


Or even in the eyes of your children or grandchildren, &nbsp;if you teach them at home.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;At the end, &nbsp;I think that I will not make a mistake if I say 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;that this way is not only the &nbsp;DESIRED &nbsp;method of solution, 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;but also is the &nbsp;EXPECTED &nbsp;way to solve this problem.