Given the binary search algorithm, answer the following questions. For those referencing a list, use the following list: $2,5,12,33,45,57,77,98,101,102$

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a$)$ How many list items will be checked to find $33?$

b$)$ How many list items will be checked to find $77?$

c$)$ How many list items will be checked to determine $75$ isn't in the list?

d$)$ Given a list of $8$ items, how many comparisons would be completed if the item was the smallest in the list?$$