Question

There are 4 people eligible to receive awards: Anne (A), Bob (B), Carol (C), and Dave (D). Suppose that two identical awards of $50 each are to be given out, and a person may receive more than one award. Write out an appropriate sample space for this experiment.

a) {A, B, C, D}
b) {AA, BB, CC, DD, AB, AC, AD, BC, BD, CD}
c) {AB, AC, AD, BC, BD, CD}
d) {AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD, DC}
e) {AA, BB, CC, DD, AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD, DC}

Answer 1

The correct sample space for the experiment in which two identical awards may be given to any one of four people, with the possibility of one person receiving both, is a complete list of combinations where order matters.

Step-by-step explanation:

The appropriate sample space for the experiment where there are 4 people eligible to receive any one of the two identical awards, and a person may receive more than one award, is option (e): {AA, BB, CC, DD, AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD, DC}. The reason this is the correct sample space is that each person can receive either one of the awards or both; hence, combinations such as 'AB' and 'BA' are distinct since they represent the different sequences in which the two people could have received the awards.