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

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 0.25 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.

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.
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Answer 1

To determine the correct graph modeling the expected probability of each outcome when selecting a number from the sample space \( S = \{1, 2, 3, 4, 5\} \), we need to calculate the probability of each outcome.

Since there are 5 equally likely outcomes (1, 2, 3, 4, 5), the probability for each outcome is given by:

\[
P(X) = \frac{1}{\text{Number of outcomes}} = \frac{1}{5} = 0.2
\]

Given this probability of \( 0.2 \) for outcomes 1 through 5, we need a bar chart where the y-axis reflects that probability.

Now, let’s evaluate the options:

1. **First option:**
- Y-axis ranges from 0 to 2.5 in increments of 0.5.
- Since the probability is 0.2, this graph is inappropriate because the maximum value goes well beyond 0.2.

2. **Second option:**
- Y-axis ranges from 0 to 6 in increments of 1.
- Similar to the first, this is much too high for our probability of 0.2.

3. **Third option:**
- Y-axis ranges from 0 to 0.25 in increments of 0.05.
- This option includes 0.2, making it a good candidate because 0.2 falls within 0.0 to 0.25.

4. **Fourth option:**
- Y-axis ranges from 0 to 0.12 in increments of 0.02.
- This won't work because 0.2 exceeds the maximum value of 0.12.

Based on this assessment, the correct graph that models the expected probability of \( 0.2 \) for each outcome is the **third option**, which has a y-axis ranging from 0 to 0.25.