Randomly choosing two potential clients for this task, you’ll use the same set of eight potential clients: jacob, carol, geraldo, meg, earvin, dora, adam, and sally. you have decided to just randomly choose two of them to offer life insurance policies. how many pairs of potential clients can be randomly chosen from the pool of eight candidates? what is the probability of any particular pair being chosen? what is the probability that the pair chosen is jacob and meg or geraldo and sally? what is the sample space of the pairs of potential clients that could be chosen?

Let Jacob, Carol, Geraldo, Meg, Earvin, Dora, Adam, and Sally be represented by the letters J, C, G, M, E, D, A, and S respectively. 

In part IV we are asked:

What is the sample space of the pairs of potential clients that could be chosen?

Since the Sample Space is the set of all possible outcomes, we need to make a set (a list) of all the possible pairs, which are as follows:

{(J, C), (J, G), (J, M), (J, E), (J, D), (J, A), (J, S)

          , (C, G), (C, M), (C, E), (C, D), (C, A), (C, S)
                   
                      , (G, M), (G, E), (G, D), (G, A), (G, S)
             
                                    ,(M, E), (M, D), (M, A), (M, S)    
 
                                               , (E, D),  (E, A),  (E, S)    
                                                          
                                                           , (D, A), (D, S)
              
                                                                       , (A, S).}

We can check that the number of the elements of the sample space, n(S) is 

1+2+3+4+5+6+7=28.

This gives us the answer to the first question: How many pairs of potential clients can be randomly chosen from the pool of eight candidates? 

( 28.)

II) What is the probability of any particular pair being chosen?

The probability of a particular pair to be picked is 1/28, as there is only one way of choosing a particular pair, out of 28 possible pairs.

III) What is the probability that the pair chosen is Jacob and Meg or Geraldo and Sally? 

The probability of choosing (J, M) or (G, S) is 2 out of 28, that is 1/14.

Answers:

I) 28
II) 1/28≈0.0357
III) 1/14≈0.0714
IV)

{(J, C),  (J, G), (J, M),  (J, E),   (J, D),  (J, A),   (J, S)
          , (C, G), (C, M), (C, E),   (C, D), (C, A),  (C, S)
                      , (G, M), (G, E),  (G, D), (G, A),  (G, S)
                                   ,(M, E),  (M, D), (M, A),  (M, S)    
                                               , (E, D),  (E, A),  (E, S)    
                                                            , (D, A), (D, S)
                                                                        , (A, S).}