What is the relationship between events A and B if they are defined as complementary?

What is the relationship between events A and B if they are defined as complementary?

• A. They can occur together
• B. At least one of them must occur
• C. One must occur, and the other cannot
• D. They are independent

Answer: (C)

When events A and B are defined as complementary, it means that if event A occurs, event B cannot occur, and vice versa. This is based on the fundamental definition of complementary events in probability theory, which states that the sum of the probabilities of complementary events equals one. Thus, their combined probabilities cover all possible outcomes in a given scenario. For example, if event A represents the occurrence of a certain outcome, event B represents the absence of that outcome. Therefore, if A happens (like flipping heads on a coin), B (flipping tails) cannot happen at the same time. Hence, it is correct to say that one must occur while the other cannot. This relationship distinctly characterizes complementary events and leads to the answer being "One must occur, and the other cannot."

When events A and B are defined as complementary, it means that if event A occurs, event B cannot occur, and vice versa. This is based on the fundamental definition of complementary events in probability theory, which states that the sum of the probabilities of complementary events equals one. Thus, their combined probabilities cover all possible outcomes in a given scenario.

For example, if event A represents the occurrence of a certain outcome, event B represents the absence of that outcome. Therefore, if A happens (like flipping heads on a coin), B (flipping tails) cannot happen at the same time. Hence, it is correct to say that one must occur while the other cannot. This relationship distinctly characterizes complementary events and leads to the answer being "One must occur, and the other cannot."