$$ \begin{array}{|c|c|c|c|} \hline & \text{Type A} & \text{Type B}& \text{Type C} \\ \hline \text{Category 1} & 12 & 34 & 16 \\ \hline \text{Category 2} & 15 & 46 & 25 \\ \hline \text{Category 3} & 3 & 14 & 20 \\ \hline \end{array} $$

The table above summarizes items by type and category. What is the probability that the selected item will not be in category 2?

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We can manually count the total number of items not in category 2 and divide that by the total number of items. It would help if we added rows and columns for total values:

$$ \begin{array}{|c|c|c|c|c|} \hline & \text{Type A} & \text{Type B}& \text{Type C}& \text{Total} \\ \hline \text{Category 1} & 12 & 34 & 16 & 62 \\ \hline \text{Category 2} & 15 & 46 & 25 & 86\\ \hline \text{Category 3} & 3 & 14 & 20 &37\\ \hline \text{Total} & & & &185\\ \hline \end{array} $$

The probability that is is not in category 2 can be found:

$$ \text{Probability of not category 2}= 1- \text{probability of category 2} $$ $$ = 1-\frac{86}{185} $$ $$ = \boxed{\frac{99}{185}} $$

You could also simply calculate the probability of being in category 1 and 3.