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# Probability of Events: Sum Rule

Our psychology department received a new statistics text for review. Prof. Smart in his review provided an interesting table of corrections.
Type: Alterations: 20%, Spelling 50%, Spelling and alterations: 10%.
Assuming that spelling and alterations are the only possible types of corrections, calculate the probability of spotting a correction due to an alteration error or a spelling error and the probability of detecting no correction.

#### Solution Preview

Alterations = Only alterations + Spelling and alterations
20%=Only alteration+10%
or Only alteration= 20% - 10%=10%

Spelling = Only spelling + Spelling and alterations
Or Only spelling = Spelling - Spelling and alterations
=50%-10%=40%

Total correction = Only alterations + Only spelling+ Spelling and ...

#### Solution Summary

In over 300 words, this solution illustrates how to solve these problems based on probability. The solution employs the addition rule of probability when events are not mutually exclusive.

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