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