A parent is searching online for books about dogs. The parent will keep searching until they find 3 suitable books. Suppose that the books the parent looks at each have a 45% chance of being suitable and that each book's suitability is independent from the others. Let X be the total number of books that the parent looks at. Note that X has a negative binomial distribution.

a) (4) Determine the probability that the parent looks at a total of 6 books.

b) (4) Determine the probability that the parent looks at a total of 7 books.

c) (3) Determine the mean and variance in the total number of books the parent looks at.

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