College Math Placement Practice Test

What is the total probability of all possible outcomes in a probability experiment?

1. 1

2. 0

3. 0.5

4. Depends on the experiment

The correct answer is: 1

In a probability experiment, the total probability of all possible outcomes must equal 1. This is a fundamental principle of probability theory known as the "axiom of total probability." When you conduct a probability experiment, you typically have a set of outcomes that represent all the possible scenarios or results that could occur. The probability of each individual outcome or event is measured between 0 (impossible outcome) and 1 (certain outcome). When you sum the probabilities of all the individual outcomes together, the total must equal 1, reflecting the certainty that one of those outcomes will occur. For instance, in a simple coin toss, there are two possible outcomes: heads and tails. The probability of getting heads is 0.5, and the probability of getting tails is also 0.5. When you add these probabilities together (0.5 + 0.5), you indeed get 1, affirming the essential axiom. In contrast, if the total probability were 0, it would imply that none of the outcomes could occur, which contradicts the nature of a probability experiment where at least one outcome must happen. A total probability of 0.5 does not capture the entirety of outcomes, indicating that only half of the