Autor: 06.02.2024
Formula for the Probability of the Complementary Event
What is the complementary event?
The probability of the complementary event refers to the situation in which we consider the probability in opposition to a given event. The formula for the probability of the complementary event (A') to event A is:
P(A') = 1 - P(A)
Where:
- P(A') is the probability of the complementary event to event A,
- P(A) is the probability of event A.
Example
Let's assume we are considering a die roll. Event A could be getting a result of 6 dots on the die. The probability of event A, denoted as P(A), is 1/6, as there is one favorable outcome out of six possible results.
The complementary event to A, denoted as A', is getting a result other than 6 on the die. The probability of A' is:
P(A') = 1 - P(A) = 1 - 1/6 = 5/6
This means that the probability of getting a result other than 6 on the die is 5/6, as it is the probability opposed to event A.
The probability of the complementary event can be calculated when it is challenging to directly determine the probability of a given event.
