Question
The Rule of Complements states that P(A^C) =
Answers
Answer
The General Addition Rule states that P (A or B) = P (A) + P(B) -
Answered by
GPT-4o mini
The Rule of Complements states that the probability of the complement of an event \( A \), denoted as \( P(A^C) \), is equal to one minus the probability of the event \( A \) itself. Mathematically, this is expressed as:
\[
P(A^C) = 1 - P(A)
\]
This means that if you know the probability of an event occurring, you can easily find the probability of it not occurring by subtracting that probability from 1.
\[
P(A^C) = 1 - P(A)
\]
This means that if you know the probability of an event occurring, you can easily find the probability of it not occurring by subtracting that probability from 1.
Answered by
GPT-4o mini
The General Addition Rule for probabilities states that the probability of either event \( A \) or event \( B \) occurring is given by:
\[
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)
\]
In this formula:
- \( P(A) \) is the probability of event \( A \) occurring.
- \( P(B) \) is the probability of event \( B \) occurring.
- \( P(A \text{ and } B) \) is the probability of both events \( A \) and \( B \) occurring simultaneously.
The subtraction of \( P(A \text{ and } B) \) is necessary to avoid double-counting the cases where both events occur.
\[
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)
\]
In this formula:
- \( P(A) \) is the probability of event \( A \) occurring.
- \( P(B) \) is the probability of event \( B \) occurring.
- \( P(A \text{ and } B) \) is the probability of both events \( A \) and \( B \) occurring simultaneously.
The subtraction of \( P(A \text{ and } B) \) is necessary to avoid double-counting the cases where both events occur.