If a set of mutually exclusive outcomes covers all possibilities, their probabilities sum to what value?

• A. 0
• B. 1
• C. 2
• D. -1

Answer: (B)

The idea here is that when a set of outcomes are mutually exclusive and together cover every possible result (they partition the sample space), their probabilities must add up to 1. This is because one of those outcomes will happen on every trial, so the total chance of something in that complete set occurring is exactly 1. Since the outcomes don’t overlap, you can add their probabilities directly, and the sum cannot exceed or fall short of the certainty that something in the set occurs. In other words, the total probability mass across all possible outcomes that exhaust the sample space is 1. This is also consistent with probabilities needing to be between 0 and 1, so values like 0, 2, or -1 don’t fit.