$(2$ points$)$ Using sequential search:

The probability that the item IS NOT in the array is $\frac{1}{4}.$ If the item is in the array, the

probability that the last item in the array matches the search key is $\frac{1}{8}.$ The probability that

the next to the last item of the array matches the search key is $\frac{1}{5}.$ The probability that

the item at index $($n$-2)$ matches the search key is $\frac{1}{16}.$ The probabilities matching any of the

remaining items are all equal.

$(1$ point$)$ What is the probability $($as a function of $n)$ of matching one of the $1$st through

$(n-3)nd$ items? Show all your work to get credit

$(1$ point$)$ Assuming that comparison of an array item where the search key is the basic opera$-$

tion, what is the average case complexity function for sequential search under these conditions.

Show all your work to get credit