According to the probability model presented, what is the sum of the probabilities of winning two races, winning one race, and losing both races?

The sum of the probabilities of all possible outcomes in a probability model must equal 1. In this case, the scenarios presented are mutually exclusive and collectively exhaustive, meaning that either winning two races, winning one race, or losing both races encompasses all possible outcomes.

When you consider the possible results, they can be broken down into three distinct categories:

1. Winning two races.

2. Winning one race.

3. Losing both races.

The correct answer, which states that the sum of the probabilities for these three outcomes is 1.0, reflects the foundational principle of probability that the total likelihood of all possible outcomes must equal one. This ensures that every outcome is accounted for, providing a complete view of the probability distribution in the scenario.

Thus, the selection of this answer demonstrates a proper understanding of how probabilities function within a defined model and ensures that all potential outcomes are included in the calculation.