Answer to Question #15406 in Statistics and Probability for sanio123

Question

The batteries to the remote control for your television have just run out. You find your collection of
miscellaneous “AA” batteries and grab 2 of them to replace the used ones. The box you used to fish out the replacements contained 14 batteries, but you were unaware that 3 of them were faulty and did not work.
a) If the remote control requires two good batteries to operate properly, what is the probability
that the remote control now works properly?
b) Given that the remote control is now working, what is the probability that the next two
batteries you select from your remaining stash will also work?