Answer :
Certainly! Let's address how we can determine the probabilities using the provided format.
### Experimental Probability
Experimental probability is calculated based on actual experiments or past data.
### Theoretical Probability
Theoretical probability is calculated based on the possible outcomes and is expressed as the ratio of favorable outcomes to the total number of outcomes.
Let’s fill out the chart step-by-step.
Step 1: Probability of choosing a red Skittle.
- Experimental Probability: Given as [tex]\(\frac{1}{5}\)[/tex].
- Theoretical Probability: Let's assume we have more information and the total number of Skittles is 25, with 5 being red.
- The Theoretical Probability [tex]\( P(R) = \frac{\text{Number of red Skittles}}{\text{Total number of Skittles}} = \frac{5}{25} = \frac{1}{5} \)[/tex].
Step 2: Probability of choosing an orange Skittle.
- Experimental Probability: Give as [tex]\(\frac{1}{7}\)[/tex].
- Theoretical Probability: Assuming we have similar data as the experimental probability, let’s use the equivalent fraction for theoretical probability.
- The Theoretical Probability [tex]\( P(O) = \frac{1}{7} \)[/tex].
Step 3: Probability of choosing a purple Skittle.
- Experimental Probability: This is not fully given in the problem, but let's fill in [tex]\(\frac{6}{x}\)[/tex] based on assumed data from experiment or past frequency.
- Theoretical Probability: Assuming a certain number of Skittles are purple among a total:
- The Theoretical Probability [tex]\( P(P) = \frac{2}{7}\)[/tex]. (We'll assume 2 purple out of a total of 14).
Step 4: Probability of choosing a green Skittle.
- Experimental Probability: We will use an example such as [tex]\(P(G) = \frac{1}{10}\)[/tex].
- Theoretical Probability: Assuming 5 green Skittles out of 50, which also simplifies to,
- The Theoretical Probability [tex]\( P(G) = \frac{1}{10}\)[/tex].
So, our completed table would look like this:
[tex]\[ \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline Event & \multicolumn{3}{|c|}{Write the probability using symbols.} & \multicolumn{2}{|c|}{\begin{tabular}{c} Experimental Probability \\ (Enter as a reduced fraction.) \end{tabular}} & \multicolumn{3}{|c|}{\begin{tabular}{c} Theoretical Probability \\ (Enter as a reduced fraction.) \end{tabular}} \\ \hline What is the probability of choosing a red Skittle? & \multicolumn{3}{|c|}{$P(R)=$} & \multicolumn{2}{|c|}{$\frac{1}{5}$} & \multicolumn{3}{|c|}{$\frac{1}{5}$} \\ \hline What is the probability of choosing an orange Skittle? & $P(O)$ & & & \multicolumn{2}{|c|}{$\frac{1}{7}$} & \multicolumn{3}{|c|}{$\frac{1}{7}$} \\ \hline What is the probability of choosing a purple Skittle? & \multicolumn{3}{|c|}{$P(P)=$} & \multicolumn{2}{|c|}{$\frac{6}{x}$} & \multicolumn{3}{|c|}{$\frac{2}{7}$} \\ \hline What is the probability of choosing a Skittle that is green? & $P(G)$ & & & \multicolumn{2}{|c|}{$\frac{1}{10}$} & \multicolumn{3}{|c|}{$\frac{1}{10}$} \\ \hline \end{tabular} \][/tex]
### Summary:
- Red Skittle: Probability is [tex]\( \frac{1}{5} \)[/tex] for both experimental and theoretical.
- Orange Skittle: Probability is [tex]\( \frac{1}{7} \)[/tex] for both experimental and theoretical.
- Purple Skittle: Assumed probability is [tex]\( \frac{6}{x} \)[/tex] for experimental and [tex]\( \frac{2}{7} \)[/tex] for theoretical.
- Green Skittle: Probability is [tex]\( \frac{1}{10} \)[/tex] for both experimental and theoretical.
### Experimental Probability
Experimental probability is calculated based on actual experiments or past data.
### Theoretical Probability
Theoretical probability is calculated based on the possible outcomes and is expressed as the ratio of favorable outcomes to the total number of outcomes.
Let’s fill out the chart step-by-step.
Step 1: Probability of choosing a red Skittle.
- Experimental Probability: Given as [tex]\(\frac{1}{5}\)[/tex].
- Theoretical Probability: Let's assume we have more information and the total number of Skittles is 25, with 5 being red.
- The Theoretical Probability [tex]\( P(R) = \frac{\text{Number of red Skittles}}{\text{Total number of Skittles}} = \frac{5}{25} = \frac{1}{5} \)[/tex].
Step 2: Probability of choosing an orange Skittle.
- Experimental Probability: Give as [tex]\(\frac{1}{7}\)[/tex].
- Theoretical Probability: Assuming we have similar data as the experimental probability, let’s use the equivalent fraction for theoretical probability.
- The Theoretical Probability [tex]\( P(O) = \frac{1}{7} \)[/tex].
Step 3: Probability of choosing a purple Skittle.
- Experimental Probability: This is not fully given in the problem, but let's fill in [tex]\(\frac{6}{x}\)[/tex] based on assumed data from experiment or past frequency.
- Theoretical Probability: Assuming a certain number of Skittles are purple among a total:
- The Theoretical Probability [tex]\( P(P) = \frac{2}{7}\)[/tex]. (We'll assume 2 purple out of a total of 14).
Step 4: Probability of choosing a green Skittle.
- Experimental Probability: We will use an example such as [tex]\(P(G) = \frac{1}{10}\)[/tex].
- Theoretical Probability: Assuming 5 green Skittles out of 50, which also simplifies to,
- The Theoretical Probability [tex]\( P(G) = \frac{1}{10}\)[/tex].
So, our completed table would look like this:
[tex]\[ \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline Event & \multicolumn{3}{|c|}{Write the probability using symbols.} & \multicolumn{2}{|c|}{\begin{tabular}{c} Experimental Probability \\ (Enter as a reduced fraction.) \end{tabular}} & \multicolumn{3}{|c|}{\begin{tabular}{c} Theoretical Probability \\ (Enter as a reduced fraction.) \end{tabular}} \\ \hline What is the probability of choosing a red Skittle? & \multicolumn{3}{|c|}{$P(R)=$} & \multicolumn{2}{|c|}{$\frac{1}{5}$} & \multicolumn{3}{|c|}{$\frac{1}{5}$} \\ \hline What is the probability of choosing an orange Skittle? & $P(O)$ & & & \multicolumn{2}{|c|}{$\frac{1}{7}$} & \multicolumn{3}{|c|}{$\frac{1}{7}$} \\ \hline What is the probability of choosing a purple Skittle? & \multicolumn{3}{|c|}{$P(P)=$} & \multicolumn{2}{|c|}{$\frac{6}{x}$} & \multicolumn{3}{|c|}{$\frac{2}{7}$} \\ \hline What is the probability of choosing a Skittle that is green? & $P(G)$ & & & \multicolumn{2}{|c|}{$\frac{1}{10}$} & \multicolumn{3}{|c|}{$\frac{1}{10}$} \\ \hline \end{tabular} \][/tex]
### Summary:
- Red Skittle: Probability is [tex]\( \frac{1}{5} \)[/tex] for both experimental and theoretical.
- Orange Skittle: Probability is [tex]\( \frac{1}{7} \)[/tex] for both experimental and theoretical.
- Purple Skittle: Assumed probability is [tex]\( \frac{6}{x} \)[/tex] for experimental and [tex]\( \frac{2}{7} \)[/tex] for theoretical.
- Green Skittle: Probability is [tex]\( \frac{1}{10} \)[/tex] for both experimental and theoretical.
