Read the proposition and the implication shown below. "if the lights are off, there is no one inside." which statement is a contrapositive to the proposition and logically equivalent to it?

The contrapositive switches the hypothesis and the conclusion and negates both in this form:
Statement: If A, then B
Contrapositive: If not B, then not A. 

In this case, the statement is: 
 "If the lights are off, there is no one inside."
Contrapositive:
If there is someone inside, the lights are on.