Question

qubit measurement-quantum mechanics

Answer 1

so far i did the multiplication of
\[\left(\begin{matrix}a \\ \sqrt{1-a^2}\end{matrix}\right)\left(\begin{matrix}b \space \space \sqrt{1-b^2} \ \end{matrix}\right)\]=
\[(ab)^2+2ab\sqrt{(1-a^2)(1-b^2)}+1-a^2-b^2+(ab)^2\]

Answer 2

The outcome of one measurement relative a different basis is the dot product of those two measurements
you have not done the dot product correctly