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Sagot :
To determine the probability that Gordon went to the track on a Tuesday, given that his class goes to the track 1/3 of the time and the class meets Monday through Friday, we can break down the problem into a series of steps to simulate the scenario:
1. Understand the probability of the class going to the track:
- Gordon's class goes running at the track [tex]\(\frac{1}{3}\)[/tex] of the time. This means that in a given week, the probability that his physical education class includes running at the track is [tex]\(\frac{1}{3}\)[/tex].
2. Understand the probability of a specific day:
- The class meets Monday through Friday, which equates to 5 days. Since the days of the week are equally likely, the probability of the class being on any specific day (e.g., Tuesday) is [tex]\(\frac{1}{5}\)[/tex].
3. Combine the probabilities to find the chance of going to the track on Tuesday:
- We multiply the probability of going to the track ([tex]\(\frac{1}{3}\)[/tex]) by the probability of the class being on Tuesday ([tex]\(\frac{1}{5}\)[/tex]):
[tex]\[ P(\text{Tuesday and running}) = P(\text{running}) \times P(\text{Tuesday}) = \frac{1}{3} \times \frac{1}{5} = \frac{1}{15}. \][/tex]
4. Convert the combined probability to decimal form for better understanding:
- [tex]\(\frac{1}{15} \approx 0.0667\)[/tex].
So, the final probability that Gordon's class goes to the track on Tuesday is approximately 0.0667 or [tex]\(6.67\%\)[/tex].
Based on these calculations, the simulation that would help in answering this question involves rolling a number cube to represent the fraction of days the class runs at the track and picking a marble to represent the days of the week. The most appropriate method chosen from your table would be:
[tex]\[ \text{\begin{tabular}{|c|c|} \hline Method & Count the number of times you... \\ \hline \begin{tabular}{c} Roll, pick, and replace \\ a marble 70 times. \end{tabular} & roll a 5 or 6 AND pick a yellow marble. \\ \hline \end{tabular} } \][/tex]
This method captures the dual nature of the probabilities: rolling (representing going to the track) and picking a marble (representing the specific day).
1. Understand the probability of the class going to the track:
- Gordon's class goes running at the track [tex]\(\frac{1}{3}\)[/tex] of the time. This means that in a given week, the probability that his physical education class includes running at the track is [tex]\(\frac{1}{3}\)[/tex].
2. Understand the probability of a specific day:
- The class meets Monday through Friday, which equates to 5 days. Since the days of the week are equally likely, the probability of the class being on any specific day (e.g., Tuesday) is [tex]\(\frac{1}{5}\)[/tex].
3. Combine the probabilities to find the chance of going to the track on Tuesday:
- We multiply the probability of going to the track ([tex]\(\frac{1}{3}\)[/tex]) by the probability of the class being on Tuesday ([tex]\(\frac{1}{5}\)[/tex]):
[tex]\[ P(\text{Tuesday and running}) = P(\text{running}) \times P(\text{Tuesday}) = \frac{1}{3} \times \frac{1}{5} = \frac{1}{15}. \][/tex]
4. Convert the combined probability to decimal form for better understanding:
- [tex]\(\frac{1}{15} \approx 0.0667\)[/tex].
So, the final probability that Gordon's class goes to the track on Tuesday is approximately 0.0667 or [tex]\(6.67\%\)[/tex].
Based on these calculations, the simulation that would help in answering this question involves rolling a number cube to represent the fraction of days the class runs at the track and picking a marble to represent the days of the week. The most appropriate method chosen from your table would be:
[tex]\[ \text{\begin{tabular}{|c|c|} \hline Method & Count the number of times you... \\ \hline \begin{tabular}{c} Roll, pick, and replace \\ a marble 70 times. \end{tabular} & roll a 5 or 6 AND pick a yellow marble. \\ \hline \end{tabular} } \][/tex]
This method captures the dual nature of the probabilities: rolling (representing going to the track) and picking a marble (representing the specific day).
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