Question

1. The letter tiles C, A, R, E, and S 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, develop a probability model for this experiment. Express the probability in decimal form, rounded to the nearest hundredth.

(1 point)
Responses

X C A R E S
P(X) 0.20 0.25 0.30 0.10 0.15X C A R E S P(X) 0.20 0.25 0.30 0.10 0.15

X C A R E S
P(X) 0.20 0.30 0.25 0.10 0.15X C A R E S P(X) 0.20 0.30 0.25 0.10 0.15

X C A R E S
P(X) 0.02 0.03 0.03 0.01 0.015X C A R E S P(X) 0.02 0.03 0.03 0.01 0.015

X C A R E S
P(X) 0.25 0.25 0.35 0.15 0.15

2. The sample space of an experiment is S={1, 2, 3, 4, 5} . If each outcome is equally likely to occur, which graph models the expected probability of each outcome?(1 point)
Responses

A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 2.5 in increments of 0.5.
Image with alt text: A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 2.5 in increments of 0.5.

A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 6 in increments of 1.
Image with alt text: A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 6 in increments of 1.

A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 0.12 in increments of 0.02.
Image with alt text: A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 0.12 in increments of 0.02.

A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 0.25 in increments of 0.05.
Image with alt text: A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 0.25 in increments of 0.05.
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3. Simon’s Results

Number of White Balls Selected Number of Red Balls Selected
Bowl A 5 15
Bowl B 16 4
Clark’s Results

Number of White Balls Selected Number of Red Balls Selected
Bowl A 45 55
Bowl B 60 40
Bowls A and B contain a number of white and red balls. Simon and Clark repeatedly selected a ball from both bowls and recorded the results in a table. Whose results will give you a better indication about the proportion of white and red balls in each bowl? Explain your answer.

(1 point)
Responses

Clark’s experiment. He conducted a greater number of trials than Simon.
Clark’s experiment. He conducted a greater number of trials than Simon.

Neither; they conducted the same number of trials.
Neither; they conducted the same number of trials.

Simon’s experiment. He conducted a greater number of trials than Clark.
Simon’s experiment. He conducted a greater number of trials than Clark.

Both results can be used, as they performed the experiment at random.

4. Use the table to answer the question.

Number of White Balls Selected Number of Red Balls Selected
Bowl A 5 15
Bowl B 16 4
Bowls A and B contain a number of white and red balls. Simon repeatedly selected a ball from both bowls and recorded the results in a table. Using Simon’s results, what is the experimental probability of picking a red ball from Bowl A? The answer needs to be in percent form.

(1 point)
Responses

75%
75%

25%
25%

37.5%
37.5%

78.95%

Answer 1

[AI-generated answer — Bot GPT 3.5]

25%

Answer 2

The letter tiles C, A, R, E, and S 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, develop a probability model for this experiment. Express the probability in decimal form, rounded to the nearest hundredth.

(1 point)
Responses

X C A R E S
P(X) 0.20 0.25 0.30 0.10 0.15X C A R E S P(X) 0.20 0.25 0.30 0.10 0.15

X C A R E S
P(X) 0.20 0.30 0.25 0.10 0.15X C A R E S P(X) 0.20 0.30 0.25 0.10 0.15

X C A R E S
P(X) 0.02 0.03 0.03 0.01 0.015X C A R E S P(X) 0.02 0.03 0.03 0.01 0.015

X C A R E S
P(X) 0.25 0.25 0.35 0.15 0.15

Answer 3

[AI-generated answer — Bot GPT 3.5]

The correct probability model based on the observed frequency is:

X C A R E S
P(X) 0.20 0.25 0.30 0.10 0.15

So, the probability for each letter is as follows:
- P(C) = 0.20
- P(A) = 0.25
- P(R) = 0.30
- P(E) = 0.10
- P(S) = 0.15

Answer 4

The sample space of an experiment is S={1, 2, 3, 4, 5} . If each outcome is equally likely to occur, which graph models the expected probability of each outcome?(1 point)ResponsesA bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 2.5 in increments of 0.5.Image with alt text: A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 2.5 in increments of 0.5.A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 6 in increments of 1.Image with alt text: A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 6 in increments of 1.A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 0.12 in increments of 0.02.Image with alt text: A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 0.12 in increments of 0.02.A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 0.25 in increments of 0.05.Image with alt text: A bar chart is titled: Probability Model for Selecting a Number from left bracket 1 comma 2 comma 3 comma 4 comma 5 right bracket. The x-axis shows outcomes and y-axis shows probability from 0 to 0.25 in increments of 0.05.Skip to navigation

Answer 5

[AI-generated answer — Bot GPT 3.5]

The correct graph that models the expected probability of each outcome in the sample space S={1, 2, 3, 4, 5} where each outcome is equally likely to occur is:

A bar chart titled: Probability Model for Selecting a Number from {1, 2, 3, 4, 5}. The x-axis shows outcomes {1, 2, 3, 4, 5} and the y-axis shows probability from 0 to 0.25 in increments of 0.05.

This representation ensures that each of the five outcomes has an equal probability of 0.2.

Answer 6

Simon’s Results

Number of White Balls Selected Number of Red Balls Selected
Bowl A 5 15
Bowl B 16 4
Clark’s Results

Number of White Balls Selected Number of Red Balls Selected
Bowl A 45 55
Bowl B 60 40
Bowls A and B contain a number of white and red balls. Simon and Clark repeatedly selected a ball from both bowls and recorded the results in a table. Whose results will give you a better indication about the proportion of white and red balls in each bowl? Explain your answer.

(1 point)
Responses

Clark’s experiment. He conducted a greater number of trials than Simon.
Clark’s experiment. He conducted a greater number of trials than Simon.

Neither; they conducted the same number of trials.
Neither; they conducted the same number of trials.

Simon’s experiment. He conducted a greater number of trials than Clark.
Simon’s experiment. He conducted a greater number of trials than Clark.

Both results can be used, as they performed the experiment at random.

Answer 7

[AI-generated answer — Bot GPT 3.5]

Clark's experiment will give a better indication about the proportion of white and red balls in each bowl. This is because Clark conducted a greater number of trials than Simon. More trials lead to more reliable and accurate results, making Clark's data more representative of the actual proportion of white and red balls in each bowl.

Answer 8

Clark’s experiment. He conducted a greater number of trials than Simon.

Clark’s experiment. He conducted a greater number of trials than Simon.

Neither; they conducted the same number of trials.
Neither; they conducted the same number of trials.

Simon’s experiment. He conducted a greater number of trials than Clark.
Simon’s experiment. He conducted a greater number of trials than Clark.

Both results can be used, as they performed the experiment at random.

Answer 9

[AI-generated answer — Bot GPT 3.5]

Clark’s experiment. He conducted a greater number of trials than Simon.