Correct option is (2) \(\frac{3}{4}\)
\((i)^{k_1}+(i)^{k_2}\) is non zero
\(\Rightarrow k_1: 4 \lambda_1+r_1, \quad r_1 \in\{0,1,2,3\} \)
\( K_2: 4 \lambda_2+r_2, \quad r_2 \in\{0,1,2,3\}\)
The pairs to get zero will be
\( (1,-1),(i,-i) \)
\(\Rightarrow \text { (i) }(1,-1) \text { pair } \)
\(\Rightarrow\left(r_1, r_2\right) \in\{(2,0),(0,2)\}\)
(ii) (i, -i) pair
\(\Rightarrow\left(r_1, r_2\right) \in\{(1,3),(3,1)\} \)
\(\Rightarrow \text { probablity }\left(i^{k_1}+i^{k_2} \neq 0\right) \)
\(= 1-\text { probablity }\left(i^{k_1}+i^{k_2} \neq 0\right) \)
\(= 1-\frac{4}{16}=\frac{12}{16}=\frac{3}{4}\)
