Answer :
To determine the experimental probability of Sarah ordering first during 40 restaurant visits, let's proceed through the following steps:
1. Observe the initial frequency data:
- From the initial trials, Sarah ordered first 3 times out of 7.
2. Scale the observed frequency to match the 40 total visits:
- We need to scale the observed frequency of Sarah ordering first during the initial 7 visits to match the 40 total visits.
- If Sarah ordered first 3 times out of 7 visits, we can find the equivalent frequency for 40 visits by using a ratio:
[tex]\[ \text{Scaled observed frequency} = \left(\frac{\text{Observed frequency initial}}{\text{Number of trials initial}}\right) \times \text{Total visits} \][/tex]
[tex]\[ \text{Scaled observed frequency} = \left(\frac{3}{7}\right) \times 40 \approx 17.142857142857142 \][/tex]
3. Calculate the experimental probability:
- The experimental probability is defined as the ratio of the observed frequency to the total number of trials.
- Therefore, the experimental probability of Sarah ordering first is:
[tex]\[ P(\text{Sarah}) = \frac{\text{Scaled observed frequency}}{\text{Total visits}} \][/tex]
[tex]\[ P(\text{Sarah}) = \frac{17.142857142857142}{40} \approx 0.42857142857142855 \][/tex]
Thus, the experimental probability of Sarah ordering first is approximately [tex]\(0.42857142857142855\)[/tex].
Given this probability value, let’s compare it with the provided options:
- 0.20
- 0.25
- 0.35
The closest matching option to [tex]\(0.42857142857142855\)[/tex] is not listed here directly. Therefore, based on the calculation, the experimental probability does not match any of the given multiple-choice options exactly but it best corresponds to approximately 0.43 (which would ideally be the correct choice if it was listed).
1. Observe the initial frequency data:
- From the initial trials, Sarah ordered first 3 times out of 7.
2. Scale the observed frequency to match the 40 total visits:
- We need to scale the observed frequency of Sarah ordering first during the initial 7 visits to match the 40 total visits.
- If Sarah ordered first 3 times out of 7 visits, we can find the equivalent frequency for 40 visits by using a ratio:
[tex]\[ \text{Scaled observed frequency} = \left(\frac{\text{Observed frequency initial}}{\text{Number of trials initial}}\right) \times \text{Total visits} \][/tex]
[tex]\[ \text{Scaled observed frequency} = \left(\frac{3}{7}\right) \times 40 \approx 17.142857142857142 \][/tex]
3. Calculate the experimental probability:
- The experimental probability is defined as the ratio of the observed frequency to the total number of trials.
- Therefore, the experimental probability of Sarah ordering first is:
[tex]\[ P(\text{Sarah}) = \frac{\text{Scaled observed frequency}}{\text{Total visits}} \][/tex]
[tex]\[ P(\text{Sarah}) = \frac{17.142857142857142}{40} \approx 0.42857142857142855 \][/tex]
Thus, the experimental probability of Sarah ordering first is approximately [tex]\(0.42857142857142855\)[/tex].
Given this probability value, let’s compare it with the provided options:
- 0.20
- 0.25
- 0.35
The closest matching option to [tex]\(0.42857142857142855\)[/tex] is not listed here directly. Therefore, based on the calculation, the experimental probability does not match any of the given multiple-choice options exactly but it best corresponds to approximately 0.43 (which would ideally be the correct choice if it was listed).
