Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
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 exp...Question
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 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. 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. 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.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve this problem, we need to determine the correct graph that models the expected probability of each outcome in the sample space \( S = \{1, 2, 3, 4, 5\} \).
Since each outcome is equally likely, the probability of each outcome is given by the formula:
\[
P(X = x) = \frac{1}{n}
\]
where \( n \) is the total number of outcomes. Here, \( n = 5 \) (the numbers 1 through 5). Thus, the probability of each outcome is:
\[
P(X = x) = \frac{1}{5} = 0.2
\]
Therefore, the expected probability for each of the outcomes (1, 2, 3, 4, 5) is 0.2.
Now let's analyze the graphs:
1. **Graph 1:** Shows probabilities from 0 to 6 - this range is incorrect since the probabilities exceed 1.
2. **Graph 2:** The y-axis shows probabilities from 0 to 0.25 in increments of 0.05. This is a suitable range and appears to have values of 0.2 (which corresponds to each outcome).
3. **Graph 3:** Shows probabilities from 0 to 2.5, which again exceed 1.
Based on this analysis, **Graph 2** is the correct one that models the expected probabilities for the outcomes {1, 2, 3, 4, 5}. Each outcome shown will have a height of 0.2, representing the expected probability of each outcome occurring.
Since each outcome is equally likely, the probability of each outcome is given by the formula:
\[
P(X = x) = \frac{1}{n}
\]
where \( n \) is the total number of outcomes. Here, \( n = 5 \) (the numbers 1 through 5). Thus, the probability of each outcome is:
\[
P(X = x) = \frac{1}{5} = 0.2
\]
Therefore, the expected probability for each of the outcomes (1, 2, 3, 4, 5) is 0.2.
Now let's analyze the graphs:
1. **Graph 1:** Shows probabilities from 0 to 6 - this range is incorrect since the probabilities exceed 1.
2. **Graph 2:** The y-axis shows probabilities from 0 to 0.25 in increments of 0.05. This is a suitable range and appears to have values of 0.2 (which corresponds to each outcome).
3. **Graph 3:** Shows probabilities from 0 to 2.5, which again exceed 1.
Based on this analysis, **Graph 2** is the correct one that models the expected probabilities for the outcomes {1, 2, 3, 4, 5}. Each outcome shown will have a height of 0.2, representing the expected probability of each outcome occurring.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.