[NW] Verify that the following is a probability model. What do we call the outcome “blue”?

Verified step by step guidance

1. Step 1: Verify that each probability is between 0 and 1. Check the given probabilities: 0.3, 0.15, 0, 0.15, 0.2, and 0.2. Since all are within the range [0, 1], this condition is satisfied.
2. Step 2: Verify that the sum of all probabilities equals 1. Add the probabilities: 0.3 + 0.15 + 0 + 0.15 + 0.2 + 0.2. This sum should be exactly 1 for a valid probability model.
3. Step 3: Since the sum equals 1 and all probabilities are valid, conclude that the given table represents a probability model.
4. Step 4: Identify the outcome 'blue' which has a probability of 0. In probability theory, an outcome with zero probability is called an 'impossible event' because it cannot occur.
5. Step 5: Summarize that the table is a valid probability model and that the outcome 'blue' is an impossible event.

Key Concepts

Probability Model

A probability model assigns probabilities to all possible outcomes of a random experiment. The probabilities must be between 0 and 1, and the sum of all probabilities must equal 1. This ensures the model accurately represents the likelihood of each outcome.

Outcome with Zero Probability

An outcome with zero probability means it is theoretically possible but will not occur in practice. It is still part of the sample space but has no chance of happening in the given model, such as the color 'blue' in this example.

Verification of a Probability Model

To verify a probability model, check that all probabilities are valid (between 0 and 1) and that their total sum is exactly 1. This confirms the model is consistent and complete for representing the random experiment.