There are \(10^2=100\) possible pairs they can choose. Let \(S\) and \(T\) denote the integers that Sofia and Tess, respectively, choose, so that \((S,T)\) denotes the integer pair.
The event that either \(S=T^2\) or \(S^2=T\) has 5 possible ways of occurring:
\(\{(1,1),(2,4),(4,2),(3,9),(9,3)\}\)
So the probability of this happening is \(\dfrac5{100}=\dfrac1{20}=0.05=5\%\). You're interested in the complement, which means the answer is 95%.
