If event A occurs, what is the probability of event A' occurring?

If event A occurs, what is the probability of event A' occurring?

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

Answer: (A)

The probability of event A' occurring, which is the complement of event A, can be understood through the fundamental properties of probability. The complement of an event A consists of all the outcomes in the sample space that are not in A. According to the rules of probability, the sum of the probabilities of an event and its complement must equal 1. Therefore, if event A has a probability of 1 (meaning it is certain that A occurs), then the probability of A' must be 0, reflecting that there are no outcomes left for the complement to include. This concept can be summarized mathematically as: P(A') = 1 - P(A) If P(A) is 1, then: P(A') = 1 - 1 = 0 Thus, when event A occurs with certainty, the probability of its complement, A', occurring is indeed 0. The correct choice accurately captures this principle of probability.

The probability of event A' occurring, which is the complement of event A, can be understood through the fundamental properties of probability. The complement of an event A consists of all the outcomes in the sample space that are not in A.

According to the rules of probability, the sum of the probabilities of an event and its complement must equal 1. Therefore, if event A has a probability of 1 (meaning it is certain that A occurs), then the probability of A' must be 0, reflecting that there are no outcomes left for the complement to include. This concept can be summarized mathematically as:

P(A') = 1 - P(A)

If P(A) is 1, then:

P(A') = 1 - 1 = 0

Thus, when event A occurs with certainty, the probability of its complement, A', occurring is indeed 0. The correct choice accurately captures this principle of probability.