If there are three mutually exclusive events at a branch point in an event tree, what is the sum of their probabilities?

If there are three mutually exclusive events at a branch point in an event tree, what is the sum of their probabilities?

• A. Zero
• B. One
• C. Three
• D. Pi

Answer: (B)

In probability theory, mutually exclusive events are those that cannot occur at the same time. If you have a set of mutually exclusive events, the key characteristic is that the occurrence of one event excludes the possibility of the others occurring simultaneously. Given this, the cumulative probability of all possible outcomes must equal one. When you have three mutually exclusive events at a branch point in an event tree, this means each event represents a distinct outcome where one of them must happen, while the others cannot. The total probability of all potential events in a closed system—where one event must occur—is always one. Therefore, the sum of their probabilities will be equal to one. This reflects the completeness of the probability distribution for the events being considered. In this case, only the alternative of zero would imply that no events occur at all, which does not align with the condition that one of the events must happen. The other options, three and Pi, do not reflect the foundational principles of probability in this scenario. Hence, the sum of the probabilities of the three mutually exclusive events is indeed one.

In probability theory, mutually exclusive events are those that cannot occur at the same time. If you have a set of mutually exclusive events, the key characteristic is that the occurrence of one event excludes the possibility of the others occurring simultaneously. Given this, the cumulative probability of all possible outcomes must equal one.

When you have three mutually exclusive events at a branch point in an event tree, this means each event represents a distinct outcome where one of them must happen, while the others cannot. The total probability of all potential events in a closed system—where one event must occur—is always one. Therefore, the sum of their probabilities will be equal to one. This reflects the completeness of the probability distribution for the events being considered.

In this case, only the alternative of zero would imply that no events occur at all, which does not align with the condition that one of the events must happen. The other options, three and Pi, do not reflect the foundational principles of probability in this scenario. Hence, the sum of the probabilities of the three mutually exclusive events is indeed one.