$($c$)$ Worst case vs average case ruming time.

e$.$g$.$ Suppose there are $2^n$ inputs to a certain problem. The rumning time of algorithm $$ is cxactly $2^n$ for exactly one of the inputs, and $1$ for any other input. Then, the rumning time is $O(1)$ since $2^n**\frac{1}{2^n}+1**(1-\frac{1}{2^n})2.$ Is this statement correct?

e$.$g$.$ Suppose we have $($:$1,2,$dots,$n$:$)$ with probability $1-\frac{1}{n}$ and $($:$n,n-1,n-2,$dots,$1$:$)$ with probability $\frac{1}{n}.$ Then, what is the average ruming time of Insertion sort?