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Using Calculator in Further Statistics

I was just reading through my FM revision book and they have alot of examples and pages on solving questions with all these methods that i usually use my calculator for.

For example inverse geometric on my calculator I just put in and get the answer, whereas they have a bunch of algebra and sums of series etc all to achieve the same values, and they make it out like that is the only method.

Is this revision guide slightly outdated or do I need to follow the way they do questions rather than simply plugging it into my calculator (cg-50)?

(Same with finding any P(X》Y) they switch into (1-P(X《Y)), where I just use my calculator)

Thanks in advanced!

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