Question 1193862
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<pre>

For this problem, the standard method of solution is as follows:


    the probability that each separate shot  will not hit the target is  {{{1-4/5}}} = {{{1/5}}}.


    the probability that no one of the three shots will hit the target is  {{{(1/5)^3}}} = {{{1/125}}}.


    the probability that at least one shot will hit the target is the COMPLEMENT to {{{1/125}}},  i.e.

         P = 1 - {{{1/125}}} = {{{124/125}}}.    <U>ANSWER</U>
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Solved.


MEMORIZE &nbsp;this chain of reasonings. &nbsp;It works in many other similar problems.


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To get wider look, &nbsp;see the lesson

&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> 

in this site.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Solved problems on Probability</U>". 



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.


Consider these lessons as your textbook,  &nbsp;handbook,  &nbsp;a Solutions Manual, &nbsp;tutorials and &nbsp;(free of charge)  &nbsp;home teacher.



Happy learning &nbsp;(&nbsp;!&nbsp;)



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Responding to the question in your comment:


<pre>
    Another way to solve the problem is to use the formula

          P(at least one hits) = p(hmm) + p(mhm) + p(mmh) + p(hhm) + p(hmh) + p(mhh) + p(hhh)

        = {{{3*(4/5)*(1/5)^2}}} + {{{3*(4/5)^2*(1/5)}}} + {{{(4/5)^3}}},

    where  "h"  means  "hits",  "m"  means  "misses".


    But it requires much more calculations and, THEREFORE, is not a front line formula/method.
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