At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To estimate the probability that the next three songs she plays are all country songs, we need to design a simulation that accurately represents the equal likelihood of choosing between rock and country songs.
A good simulation would involve an equal split between the two options (rock and country). Let's evaluate the given options to find the best fit.
Option A:
- Number cube (six faces).
- Even number = rock.
- Odd number = country.
- Roll the cube three times. Repeat.
Since a standard six-sided number cube has three even numbers (2, 4, 6) and three odd numbers (1, 3, 5), this approach results in an equal probability (50%) of selecting rock or country for each roll. Consistently rolling the cube three times and categorizing the results correctly achieves the goal. This is a valid simulation.
Option B:
- Random digits (0–9).
- Let [tex]$1,2,3,4,5=$[/tex] rock.
- Let [tex]$6,7,8,9=$[/tex] country.
- Select three random digits. Repeat.
Here, the probability of selecting a rock song is [tex]\(\frac{5}{10}\)[/tex] (or 50%), and the probability of selecting a country song is [tex]\(\frac{4}{10}\)[/tex] (or 40%). This design does not provide an equal likelihood for rock and country songs. This is not a valid simulation.
Option C:
- Number cube (which typically has six faces).
- Let [tex]$1=$[/tex] rock.
- Let [tex]$2=$[/tex] country.
- Roll cube three times. Repeat.
This option fails because it only specifies outcomes for two results (rock for [tex]$1$[/tex] and country for [tex]$2$[/tex]) on the number cube without consideration for the remaining four numbers ([tex]$3, 4, 5, 6$[/tex]). This is not a valid simulation.
Option D:
- Random digits.
- Let [tex]$1,2,3=$[/tex] rock.
- Let [tex]$4,5,6=$[/tex] country.
- Select three random digits. Repeat.
Here, the probability of selecting a rock song is [tex]\(\frac{3}{6}\)[/tex] (or 50%), and the probability of selecting a country song is also [tex]\(\frac{3}{6}\)[/tex] (or 50%). This approach means there is an equal chance of selecting either genre, matching the need for equal likelihood. This is a valid simulation.
Conclusion:
Both Option A and Option D provide valid ways to estimate the probability of playing three consecutive country songs because they both ensure an equal likelihood of selecting rock or country songs.
To summarize:
- Simulation Design A: Valid.
- Simulation Design D: Valid.
In the context of the question, either Option A or Option D can be used to accurately estimate the probability.
A good simulation would involve an equal split between the two options (rock and country). Let's evaluate the given options to find the best fit.
Option A:
- Number cube (six faces).
- Even number = rock.
- Odd number = country.
- Roll the cube three times. Repeat.
Since a standard six-sided number cube has three even numbers (2, 4, 6) and three odd numbers (1, 3, 5), this approach results in an equal probability (50%) of selecting rock or country for each roll. Consistently rolling the cube three times and categorizing the results correctly achieves the goal. This is a valid simulation.
Option B:
- Random digits (0–9).
- Let [tex]$1,2,3,4,5=$[/tex] rock.
- Let [tex]$6,7,8,9=$[/tex] country.
- Select three random digits. Repeat.
Here, the probability of selecting a rock song is [tex]\(\frac{5}{10}\)[/tex] (or 50%), and the probability of selecting a country song is [tex]\(\frac{4}{10}\)[/tex] (or 40%). This design does not provide an equal likelihood for rock and country songs. This is not a valid simulation.
Option C:
- Number cube (which typically has six faces).
- Let [tex]$1=$[/tex] rock.
- Let [tex]$2=$[/tex] country.
- Roll cube three times. Repeat.
This option fails because it only specifies outcomes for two results (rock for [tex]$1$[/tex] and country for [tex]$2$[/tex]) on the number cube without consideration for the remaining four numbers ([tex]$3, 4, 5, 6$[/tex]). This is not a valid simulation.
Option D:
- Random digits.
- Let [tex]$1,2,3=$[/tex] rock.
- Let [tex]$4,5,6=$[/tex] country.
- Select three random digits. Repeat.
Here, the probability of selecting a rock song is [tex]\(\frac{3}{6}\)[/tex] (or 50%), and the probability of selecting a country song is also [tex]\(\frac{3}{6}\)[/tex] (or 50%). This approach means there is an equal chance of selecting either genre, matching the need for equal likelihood. This is a valid simulation.
Conclusion:
Both Option A and Option D provide valid ways to estimate the probability of playing three consecutive country songs because they both ensure an equal likelihood of selecting rock or country songs.
To summarize:
- Simulation Design A: Valid.
- Simulation Design D: Valid.
In the context of the question, either Option A or Option D can be used to accurately estimate the probability.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
