joels living room wall is 13ft long with 2 inch wide vertical support beams every 16 inches, starting at the right edge of the wall. If Joel wants to hang a mirror that is secured to one of the support beams what are the chances that a randomly placed nail will go through a beam

We won't simply provide an answer for your homework problem, but are happy to help you through it. First step: determine how many of these 2" wide support beams are present on the 13' wall. What do you calculate for that?