Let's go through the correct binary search process step by step for the key $15$ in the given keys array $\{10,20,30,40,50,60,70\}$:

Initial values: lo $=0,$ hi $=6$

First iteration:

mid $=($lo $+$ hi$)/2=3$

keys$[$mid$]=40$

Since $15<40,$ we update hi to mid $-1,$ becoming hi $=2.$

Second iteration:

mid $=($lo $+$ hi$)/2=1$

keys$[$mid$]=20$

Since $15>20,$ we update lo to mid $+1,$ becoming lo $=2.$

Final iteration:

lo $=2,$ hi $=2$

mid $=($lo $+$ hi$)/2=2$

keys$[$mid$]=30$

Since $15<30,$ we update hi to mid $-1,$ becoming hi $=1.$

The search stops at this point because lo becomes greater than hi$.$ The final values are lo $=2$ and hi $=1.$ The key $15$ is not found in the keys array, and the final value of hi indicates the position before which $15$ should be inserted to maintain the sorted order $($the index before which it should be inserted$).$ I appreciate your understanding.