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).

Answer 1

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

1. All outcomes have the same probability.

   • This is true for a uniform probability model, as all outcomes must have equal likelihood.

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

   • This is a general requirement for all probability models, not just uniform ones. However, it must still be true.

3. The sum of the probabilities is 1.

   • This is a fundamental property of all probability models and must be satisfied.

The statement "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)" describes the expected value concept, which is indeed true for any probability model but doesn't necessarily define a uniform probability model.

Thus, the statements that MUST be true for a uniform probability model are:

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