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Experimental Probability Theory
![We can calculate the experimental probability by physically testing the expected outcomes. This is called experimental probability. \\ Experimental probability has the following formula\\ \(P(E)=\dfrac{\text { The number of times event " } E \text { " has happened }}{\text { The total number of trials }}\)\\ OR\\ \(P(E)=\dfrac{\text { frequency of " } E \text { " }}{\text { total frequency }}\)\\ Frequency \(=\) Number of times something happens \\ \textbf{Example}\\ Two dice were rolled and summed up as part of an experiment, the results are shown in the table below. $$\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|} \hline \text { Outcome } & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline \text { Frequency } & 0 & 2 & 4 & 4 & 5 & 7 & 6 & 4 & 4 & 3 & 1 \\ \hline \end{array}$$ From the table, calculate the following probabilities.\\ \textbf{i)} Getting a sum of 10 \\ \textbf{ii)} Getting a sum that is odd.\\ \textbf{iii)} Getting a sum that is less than 6\\ \textbf{Example 1 solution}\\ $\begin{aligned} \textbf{i) }& \begin{aligned}[t] \text { Total frequencys } & =0+2+4+4+5+7+6+4+4+3+1 \\ & =40 \end{aligned}\\ &\begin{aligned} P(10) & =\frac{4}{40} \\ & =\frac{1}{10} \end{aligned}\\ \textbf{ii) } & \begin{aligned}[t] P(\text { odd })=P(3,5,7,9,11) & =\frac{2+4+7+4+3}{40} \\ & =\frac{20}{40} \\ & =\frac{1}{2} \end{aligned}\\ \textbf{iii) } & \begin{aligned}[t] P(\text { less than } 6)=P(2,3,4,5) & =\frac{0+2+4+4}{40} \\ & =\frac{10}{40} \\ & =\frac{1}{4} \end{aligned} \end{aligned}$](/media/u5rpwpbe/9247.png)
NSW Y8 Maths Probability Experimental Probability
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