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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

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 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.

2.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.

3.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.

4.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.

1 answer

To determine which graph accurately represents the expected probability of each outcome from the sample space \( S = {1, 2, 3, 4, 5} \), we need to calculate the probability for each outcome.

Since each outcome is equally likely, the probability of each outcome is given by:

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

Now, we need to evaluate the options based on this probability:

  1. First Option: The y-axis ranges from 0 to 6. This range is not suitable because the probabilities cannot exceed 1.

  2. Second Option: The y-axis ranges from 0 to 2.5. Again, this range is too high for probabilities.

  3. Third Option: The y-axis ranges from 0 to 0.25 (in increments of 0.05). Since \( 0.2 \) is within this range, this option could be correct.

  4. Fourth Option: The y-axis ranges from 0 to 0.12. This range is too low for the probability of 0.2.

The correct graph that models the expected probability of each outcome from the set \( S = {1, 2, 3, 4, 5} \) would be the third option, as it adequately represents probabilities around the value of 0.2.