The tv remote in your house takes two AA batteries and both batteries must not be dead for the remote to work properly. You have a box of new batteries, but you know that your roommate accidentally put some dead batteries in the box. Now they're all mixed up- a total of 15 batteries, and four of them are dead. You reach in to grab two of them. Find the following probabilities
a. both batteries are new
b. both batteries are dead
c. at least one battery is dead