Answer :
To determine whose results provide the best estimate of the probability of rolling a 6 with the dice, we can analyze the recorded data from Hollie, Izzy, and Jess.
First, let's calculate the probability [tex]\( P \)[/tex] of rolling a 6 for each person:
1. Hollie:
- Number of rolls: 20
- Number of 6s: 1
- Probability of rolling a 6 = [tex]\(\frac{\text{Number of 6s}}{\text{Number of rolls}}\)[/tex] = [tex]\(\frac{1}{20} = 0.05\)[/tex]
2. Izzy:
- Number of rolls: 50
- Number of 6s: 14
- Probability of rolling a 6 = [tex]\(\frac{14}{50} = 0.28\)[/tex]
3. Jess:
- Number of rolls: 200
- Number of 6s: 31
- Probability of rolling a 6 = [tex]\(\frac{31}{200} = 0.155\)[/tex]
Now, we have the following probabilities:
- Hollie: 0.05
- Izzy: 0.28
- Jess: 0.155
When comparing these probabilities, an important factor to consider is the number of trials (rolls). Generally, the more trials conducted, the better the estimate of the true probability, due to the Law of Large Numbers. In this case:
- Hollie rolled the dice 20 times.
- Izzy rolled the dice 50 times.
- Jess rolled the dice 200 times.
Since Jess has the largest number of rolls (200), her results are based on a much larger sample size compared to Hollie and Izzy. This larger sample size means Jess's estimate is less likely to be influenced by random variations and provides a more reliable estimate of the probability of rolling a 6.
Therefore, Jess's results give the best estimate of the probability of rolling a 6 with this dice. Her larger number of rolls makes her estimate more reliable and representative of the actual probability.
First, let's calculate the probability [tex]\( P \)[/tex] of rolling a 6 for each person:
1. Hollie:
- Number of rolls: 20
- Number of 6s: 1
- Probability of rolling a 6 = [tex]\(\frac{\text{Number of 6s}}{\text{Number of rolls}}\)[/tex] = [tex]\(\frac{1}{20} = 0.05\)[/tex]
2. Izzy:
- Number of rolls: 50
- Number of 6s: 14
- Probability of rolling a 6 = [tex]\(\frac{14}{50} = 0.28\)[/tex]
3. Jess:
- Number of rolls: 200
- Number of 6s: 31
- Probability of rolling a 6 = [tex]\(\frac{31}{200} = 0.155\)[/tex]
Now, we have the following probabilities:
- Hollie: 0.05
- Izzy: 0.28
- Jess: 0.155
When comparing these probabilities, an important factor to consider is the number of trials (rolls). Generally, the more trials conducted, the better the estimate of the true probability, due to the Law of Large Numbers. In this case:
- Hollie rolled the dice 20 times.
- Izzy rolled the dice 50 times.
- Jess rolled the dice 200 times.
Since Jess has the largest number of rolls (200), her results are based on a much larger sample size compared to Hollie and Izzy. This larger sample size means Jess's estimate is less likely to be influenced by random variations and provides a more reliable estimate of the probability of rolling a 6.
Therefore, Jess's results give the best estimate of the probability of rolling a 6 with this dice. Her larger number of rolls makes her estimate more reliable and representative of the actual probability.
