Consider the Additional Notes for Lesson 4 on the Study Guide. Choose the statements below that MUST be true for a probability model to be uniform.(1 point)

Question

Responses

All outcomes have the same probability.
All outcomes have the same probability.

The probability of each outcome is between 0 and 1.
The probability of each outcome is between 0 and 1.

The sum of the probabilities is 1.
The sum of the probabilities is 1.

If the experiment is done repeatedly for n trials, then the expected number of times each outcome E would happen is given by n·(E).
If the experiment is done repeatedly for n trials, then the expected number of times each outcome E would happen is given by n·(E).

All of the above.

Answer 1

For a probability model to be uniform, the following statements must be true:

1. All outcomes have the same probability.
2. The probability of each outcome is between 0 and 1.
3. The sum of the probabilities is 1.

While the statement regarding the expected number of times each outcome E would happen (given by n·(E)) is related, it is not a defining characteristic of a uniform probability model—it is a consequence of the previous statements when considering a large number of trials.

Therefore, the correct answer that includes all statements that must be true for a uniform probability model is:

1. All outcomes have the same probability.
2. The probability of each outcome is between 0 and 1.
3. The sum of the probabilities is 1.

The response "All of the above" is not entirely accurate because the last statement does not strictly define a uniform probability model. Instead, the first three statements must be true.