Question

The letter tiles , , , , and are placed in a box. Without looking, Jorelle picks a letter tile from

the box and records the result before placing it back. He repeats the procedure 100 times and
observes the following results:
Outcomes C A R E S
Frequency 20 25 30 10 15
Based on the observed frequency, what is the probability that Jorelle will pick a letter ? The answer
should be in percent form.
(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The total number of outcomes is 100, and the frequency of picking the letter R is 30.

The probability of picking the letter R is:
P(R) = Frequency of R / Total number of outcomes
P(R) = 30 / 100
P(R) = 0.3 or 30%

Therefore, the probability that Jorelle will pick the letter R is 30%.

Answer 2

Use the table to answer the question.

Outcomes 2 4 6 8 10 12
Frequency 10 9 6 15 13 8
Jede tossed a cube with faces numbered with 2, 4, 6, 8, 10, and 12. The results are recorded in the
table. What is the largest discrepancy between the experimental and the expected probability of this
experiment? The answer needs to be in percent form to the nearest whole number.
(1 point

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the largest discrepancy between the experimental and expected probability, we first need to calculate the expected probability for each outcome based on the total number of outcomes.

Total number of outcomes = 10 + 9 + 6 + 15 + 13 + 8 = 61

Now, calculate the expected probability for each outcome:

Expected probability for 2 = 10 / 61 ≈ 0.164
Expected probability for 4 = 9 / 61 ≈ 0.148
Expected probability for 6 = 6 / 61 ≈ 0.098
Expected probability for 8 = 15 / 61 ≈ 0.246
Expected probability for 10 = 13 / 61 ≈ 0.213
Expected probability for 12 = 8 / 61 ≈ 0.131

Now, we need to compare the experimental and expected probabilities to find the largest discrepancy:

The largest discrepancy occurs when comparing the experimental probability of 6 (6/61 ≈ 0.098) and the expected probability of 8 (15/61 ≈ 0.246).

The discrepancy is approximately:
0.246 - 0.098 = 0.148

To convert this discrepancy to percentage, multiply by 100:
0.148 * 100 ≈ 14.8%

Therefore, the largest discrepancy between the experimental and expected probability in this experiment is 15%.

Answer 4

wrong

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize for the error in my previous response. Let's correct this calculation:

The expected probability for each outcome can be calculated by dividing the frequency of each outcome by the total number of outcomes (61 in this case):

Expected probability for 2: 10/61 ≈ 0.164
Expected probability for 4: 9/61 ≈ 0.148
Expected probability for 6: 6/61 ≈ 0.098
Expected probability for 8: 15/61 ≈ 0.246
Expected probability for 10: 13/61 ≈ 0.213
Expected probability for 12: 8/61 ≈ 0.131

Now, we compare the experimental and expected probabilities to find the largest discrepancy:

1. For the outcome 6:
Experimental probability = 6/61 ≈ 0.098
Expected probability = 0.098

The discrepancy for this outcome is 0, as the experimental and expected probabilities match.

The largest discrepancy occurs when comparing the experimental probability for the outcome 8 (15/61 ≈ 0.246) and the expected probability for the outcome 10 (13/61 ≈ 0.213).

The discrepancy is approximately:
|0.246 - 0.213| = 0.033

To convert this discrepancy to percentage, multiply by 100:
0.033 * 100 = 3.3%

Therefore, the largest discrepancy between the experimental and expected probability in this experiment is 3.3%.

Answer 6

Use the table to answer the question.

Outcomes 2 4 6 8 10 12
Frequency 10 9 6 15 13 8
Jede tossed a cube with faces numbered with 2, 4, 6, 8, 10, and 12. The results are recorded in the
table. What is the smallest discrepancy between the experimental and the expected probability of this
experiment? Write your answer in 3 decimal places, rounded to the nearest thousandth.
(1 point)

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the smallest discrepancy between the experimental and expected probability, we need to calculate the expected probability for each outcome based on the total number of outcomes.

Total number of outcomes = 10 + 9 + 6 + 15 + 13 + 8 = 61

Now, calculate the expected probability for each outcome:

Expected probability for 2 = 10 / 61 ≈ 0.164
Expected probability for 4 = 9 / 61 ≈ 0.148
Expected probability for 6 = 6 / 61 ≈ 0.098
Expected probability for 8 = 15 / 61 ≈ 0.246
Expected probability for 10 = 13 / 61 ≈ 0.213
Expected probability for 12 = 8 / 61 ≈ 0.131

Now, compare the experimental probabilities with the expected probabilities to find the smallest discrepancy:

1. For the outcome 6:
Experimental probability = 6/61 ≈ 0.098
Expected probability = 0.098

The discrepancy for this outcome is 0, as the experimental and expected probabilities match.

The smallest discrepancy occurs when comparing the experimental probability for the outcome 4 (9/61 ≈ 0.148) and the expected probability for the outcome 2 (10/61 ≈ 0.164).

The discrepancy is approximately:
|0.148 - 0.164| = 0.016

Rounded to three decimal places, the smallest discrepancy is 0.016.

Therefore, the smallest discrepancy between the experimental and expected probability in this experiment is 0.016.