Events A and A' are what type of event according to set theory?

Events A and A' are what type of event according to set theory?

• A. Independent
• B. Exclusive
• C. Complementary
• D. Overlapping

Answer: (C)

In set theory, events A and A' refer to an event and its complement. The complement of an event A, denoted as A', includes all outcomes in the sample space that are not in A. This means that together, events A and A' encompass the entire sample space without any overlap. Thus, A and A' are considered complementary events because they are mutually exclusive; when one event occurs, the other cannot occur. The definition of complementary events specifically highlights that the probabilities of A and A' add up to 1, which is a fundamental property of probability related to complements. Moreover, this understanding is crucial in probability theory, as it enables the calculation of event probabilities and contributes to more complex calculations involving unions and intersections of events.

In set theory, events A and A' refer to an event and its complement. The complement of an event A, denoted as A', includes all outcomes in the sample space that are not in A. This means that together, events A and A' encompass the entire sample space without any overlap.

Thus, A and A' are considered complementary events because they are mutually exclusive; when one event occurs, the other cannot occur. The definition of complementary events specifically highlights that the probabilities of A and A' add up to 1, which is a fundamental property of probability related to complements.

Moreover, this understanding is crucial in probability theory, as it enables the calculation of event probabilities and contributes to more complex calculations involving unions and intersections of events.