Statistic Sample Question

Question

Suppose that you bought a package of 5 generic batteries for a new shower radio you received as a gift. However, unknown to you, one of the five batteries is defective (will not transfer any current) and the other four are good. You choose two of the five batteries at random to use in your new radio. Write the sample space for this problem.

Answer 1

I usually approach these sort of problems by drawing a diagram to help me sort things out.  I'll use G for good and D for defective.  I'll list the pairs of possible choices by writing what's possible for the first draw to the left (5 choices), then what is possible for the second draw on the right (4 choices).  The key here is to think about the fact that all of the good batteries are really unique -- kind of like if they each looked different (like a brand label) or something like that, and not just Good.

   →G

G →G

   →G    

   →D

 

 

   →G
G →G
   →G
   →D

 

   →G
G →G
   →G
   →D

 

   →G
G →G
   →G
   →D

 

   →G
D →G
   →G
   →G

So the sample space for this problem looks like all twenty of these written out and put inside braces, each separated by commas.  These don't have to be in any particular order as long as you've written out all of the individual possible outcomes, even if they repeat, like this one does quite a lot!  Not very exciting for a problem, but it should show you why the same space is much more than {G-G, G-D}.