Subjects algebra

Counts Simplification E7D15F

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Counts Simplification E7D15F


1. The problem asks how to simplify a formula when using counts instead of probabilities. 2. Probabilities are often calculated as counts divided by total counts, i.e., $p = \frac{count}{total}$. 3. If the formula uses probabilities, replacing them with counts means substituting $p$ with $\frac{count}{total}$. 4. To simplify, multiply through by the total to eliminate denominators. 5. For example, if the formula is $p_1 \times p_2$, replacing with counts gives $\frac{count_1}{total} \times \frac{count_2}{total} = \frac{count_1 \times count_2}{total^2}$. 6. Multiplying both sides by $total^2$ simplifies the expression to $count_1 \times count_2$. 7. Thus, using counts directly often means scaling the formula by powers of the total count to clear denominators. 8. This simplification is useful when working with raw data counts instead of normalized probabilities.