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 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 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 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 0.12 in increments of 0.02. Skip to navigation
Answers
Answered by
GPT-4o mini
To determine the expected probability of each outcome in the sample space \( S = \{1, 2, 3, 4, 5\} \), we first recognize that each outcome is equally likely. Therefore, the probability of each outcome can be calculated by dividing the total number of outcomes by the number of possible outcomes.
There are 5 outcomes in total, so the probability \( P \) of each outcome is:
\[
P(\text{each outcome}) = \frac{1}{5} = 0.2
\]
Considering this, the expected probability for each of the outcomes 1, 2, 3, 4, and 5 is \( 0.2 \).
Now, we need to find the graph that appropriately represents this probability.
Looking at the options you provided:
1. The first graph has a y-axis that ranges from 0 to 2.5, which is too large since the probabilities should only range between 0 and 1.
2. The second graph has a y-axis from 0 to 0.25 in increments of 0.05. \( 0.2 \) fits within this range.
3. The third graph has a y-axis from 0 to 6, which is again too large.
4. The fourth graph has a y-axis from 0 to 0.12 in increments of 0.02, which does not reach \( 0.2 \).
Thus, the correct graph that models the expected probability of each outcome is:
**The second graph**: A bar chart with a y-axis ranging from 0 to 0.25 in increments of 0.05, where the height of each bar is \( 0.2 \).
There are 5 outcomes in total, so the probability \( P \) of each outcome is:
\[
P(\text{each outcome}) = \frac{1}{5} = 0.2
\]
Considering this, the expected probability for each of the outcomes 1, 2, 3, 4, and 5 is \( 0.2 \).
Now, we need to find the graph that appropriately represents this probability.
Looking at the options you provided:
1. The first graph has a y-axis that ranges from 0 to 2.5, which is too large since the probabilities should only range between 0 and 1.
2. The second graph has a y-axis from 0 to 0.25 in increments of 0.05. \( 0.2 \) fits within this range.
3. The third graph has a y-axis from 0 to 6, which is again too large.
4. The fourth graph has a y-axis from 0 to 0.12 in increments of 0.02, which does not reach \( 0.2 \).
Thus, the correct graph that models the expected probability of each outcome is:
**The second graph**: A bar chart with a y-axis ranging from 0 to 0.25 in increments of 0.05, where the height of each bar is \( 0.2 \).
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