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Ginger buys lunch at school every day. She always gets pizza when it is available. The cafeteria has pizza about 80% of the time.

Ginger runs a simulation to model this using a random number generator. She assigns these digits to the possible outcomes for each day of the week:
- Let 0 and 1 = no pizza available
- Let 2, 3, 4, 5, 6, 7, 8, and 9 = pizza available

The table shows the results of the simulation.

| 08458 | 47165 | 68194 | 88490 | 01841 |
|-------|-------|-------|-------|-------|
| 43226 | 12924 | 52568 | 93039 | 39406 |

What is the estimated probability that Ginger will eat pizza for lunch every day next week?

Sagot :

GinnyAnswer
To determine the estimated probability that Ginger will eat pizza for lunch every day of the week, we need to analyze the simulated data and calculate the frequency with which pizza is available every day in a week.

Given the simulated data:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline 08458 & 47165 & 68194 & 88490 & 01841 \\ \hline 43226 & 12924 & 52568 & 93039 & 39406 \\ \hline \end{tabular} \][/tex]

In these table entries:
- The digits 0 and 1 represent days when there is no pizza available.
- The digits 2 through 9 represent days when pizza is available.

Let's analyze each week to determine if pizza is available every day (i.e., no digit 0 or 1 in a week):

1. Week 1: 08458
- Contains digits 0 and 1, meaning no pizza on those days.
- Pizza is not available every day this week.

2. Week 2: 47165
- Contains digit 1, meaning no pizza on that day.
- Pizza is not available every day this week.

3. Week 3: 68194
- Contains digit 1, meaning no pizza on that day.
- Pizza is not available every day this week.

4. Week 4: 88490
- Contains digit 0, meaning no pizza on that day.
- Pizza is not available every day this week.

5. Week 5: 01841
- Contains digits 0 and 1, meaning no pizza on those days.
- Pizza is not available every day this week.

6. Week 6: 43226
- All digits are 2-6, indicating pizza is available every day.
- Pizza is available every day this week.

7. Week 7: 12924
- Contains digit 1, meaning no pizza on that day.
- Pizza is not available every day this week.

8. Week 8: 52568
- All digits are 2-8, indicating pizza is available every day.
- Pizza is available every day this week.

9. Week 9: 93039
- Contains digit 0, meaning no pizza on that day.
- Pizza is not available every day this week.

10. Week 10: 39406
- Contains digit 0, meaning no pizza on that day.
- Pizza is not available every day this week.

Now, we count the number of weeks where pizza was available every day:

- Total number of weeks simulated: 10
- Number of weeks with pizza every day: 2

To find the estimated probability that Ginger will eat pizza for lunch every day next week, we use the ratio of the favorable outcomes to the total trials:

[tex]\[ \text{Estimated Probability} = \frac{\text{Number of Weeks with Pizza Every Day}}{\text{Total Number of Weeks}} \][/tex]

[tex]\[ \text{Estimated Probability} = \frac{2}{10} = 0.2 \][/tex]

Therefore, the estimated probability that Ginger will eat pizza for lunch every day next week is [tex]\( 0.2 \)[/tex] or [tex]\( 20\% \)[/tex].
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