Question 1118905
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<pre>
Time interval duration "between 11 minutes and 21 minutes" is 10 minutes:

     1 minute from 11 min. to 12 min.
     1 minute from 12 min. to 13 min.
     1 minute from 13 min. to 14 min.
     1 minute from 14 min. to 15 min.
     1 minute from 15 min. to 16 min.
     1 minute from 16 min. to 17 min.
     1 minute from 17 min. to 18 min.
     1 minute from 18 min. to 19 min.
     1 minute from 19 min. to 20 min.
     1 minute from 20 min. to 21 min.


Time interval duration "between 13 minutes and 19 minutes" is 6 minutes:

     1 minute from 13 min. to 14 min.
     1 minute from 14 min. to 15 min.
     1 minute from 15 min. to 16 min.
     1 minute from 16 min. to 17 min.
     1 minute from 17 min. to 18 min.
     1 minute from 18 min. to 19 min.


The probability under the question is the ratio of 6 minutes to 10 minutes  {{{6/10}}} = 0.6 = 60%.
</pre>

Solved.


The solution and the answer by the other tutor are incorrect.


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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;After reading the @greenestamps solution I added this <U>NOTICE</U>.



The meaning of this problem is <U>THIS</U>:


<pre>
    I have a stop watch. I turn it on when I start dish washing, and I stop it when the process ends.


    I write the reading of the stop watch after every/each experiment.


    Then I see that the readings for the process duration are uniformly distributed over the time interval <U>between</U> 11 minutes 
    (=from the start of the 11-th minute reading) and 21 minutes (=to the complete end of the 20-th minute, 
    i.e. to the moment, when 21-th minute starts).


     . . . And so on to the end of the condition.
</pre>


    This problem &nbsp;HAS &nbsp;THIS &nbsp;and &nbsp;ONLY &nbsp;THIS &nbsp;reading and meaning.


     Nothing else.  &nbsp;&nbsp;// &nbsp;&nbsp;The words &nbsp;"<U>uniformly distributed</U>" &nbsp;of the condition do not leave the place (the gap) for any other interpretation.


     Any different interpretation is &nbsp;FALSE &nbsp;and &nbsp;IRRELEVANT.


     In particular, &nbsp;the proposed by &nbsp;@greenestamps &nbsp;interpretation is wrong.



I agree that the problem formulation is not perfect, since it does not determine if 21-th minute is included completely or not.  


If it is included (as well as the 19-th minutes is fully included), then the answer is  {{{7/11}}}.


But in any case two continuous time intervals are considered, and there is no place for a "discrete" interpretation.


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


It is a STANDARD introductory problem on geometric probability.


To see other similar solved problems, &nbsp;look into the lesson

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

in this site.