Apply class on based on nth-child selection

Question

I have the following list:

<ul class="border">
  <li>test1</li>
  <li class="selected">test2</li>
  <li>test3</li>
</ul>

Is it possible to use sass for

.border {

  &.li:nth-child(3).selected {
      make background color of .border black
  }

}

Couldn't figure this out.