What is the sum of the probabilities P(A) and P(A')?

What is the sum of the probabilities P(A) and P(A')?

• A. 1
• B. 0
• C. 0.5
• D. Depends on A

Answer: (A)

The sum of the probabilities P(A) and P(A') equals 1 due to the fundamental properties of probability theory. Here, P(A) represents the probability of event A occurring, while P(A') is the probability of event A not occurring, referred to as the complement of A. According to the law of total probability, the outcomes of a statistical experiment must include all possible events, which can be either A or its complement A'. Since these two events (A and A') encompass the entire sample space, their probabilities must sum to 1: P(A) + P(A') = 1. This principle is a foundational concept in probability, ensuring that when you take into account both the event and its complement, you capture all potential outcomes of the experiment. Therefore, the choice stating that the sum is 1 is indeed the correct interpretation of the relationship between an event and its complement in probability.

The sum of the probabilities P(A) and P(A') equals 1 due to the fundamental properties of probability theory. Here, P(A) represents the probability of event A occurring, while P(A') is the probability of event A not occurring, referred to as the complement of A. According to the law of total probability, the outcomes of a statistical experiment must include all possible events, which can be either A or its complement A'.

Since these two events (A and A') encompass the entire sample space, their probabilities must sum to 1:

P(A) + P(A') = 1.

This principle is a foundational concept in probability, ensuring that when you take into account both the event and its complement, you capture all potential outcomes of the experiment. Therefore, the choice stating that the sum is 1 is indeed the correct interpretation of the relationship between an event and its complement in probability.