Question 1137840
.
Shortly saying,


<pre>  
(a)  the sample space is the space of all subsets of the given set, consisting of 2 elements,  or, in other words,


     The sample space is the set of all pairs (X,Y), where X and Y are different names from the given list of companies.


     In combinatorics, such type of sets is calling "combinations of 5 names of the companies taken 2 at a time".


     The number of elements in the sample space is  {{{C[3+2]^2}}} = {{{C[5]^2}}} = {{{(5*4)/(1*2)}}} = 10.



(b)  Investor can select 2 of the 3 industrial stokes by  {{{C[3]^2}}} = {{{(3*2)/(1*2)}}} = {{{6/2}}} = 3 ways.

     So the probability of event A under question (B)  is  P(A) = {{{3/10}}} = 0.3.
</pre>

Solved.


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On Combinations, &nbsp;see introductory lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</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>Combinatorics: Combinations and permutations</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.



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This my post is not to argue with the solution by Jim Thompson, which is absolutely correct.


It is to get you familiar with the terminology and key conceptions of Combinatorics, that are adjacent to this Probability problem.