# Question Video: Determining the Probability of Complement of a Given Event Mathematics

If the probability of an event happening is 11/30, what is the probability of the event not happening?

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### Video Transcript

If the probability of an event happening is 11 out of 30 or eleven thirtieths, what is the probability of the event not happening?

We know that the probability of an event not happening is known as the complementary event. This is denoted by 𝐴 bar or 𝐴 prime, where the probability of 𝐴 bar is equal to one minus the probability of 𝐴. In this question, we are told the probability of the event happening is 11 out of 30. If we let this be event 𝐴, then the probability of 𝐴 is equal to eleven thirtieths or 11 out of 30. We can then calculate the probability of the event not happening by subtracting this from one. One whole one is the same as 30 out of 30 or thirty thirtieths. As the denominators are the same, we simply subtract the numerators, giving us 19 out of 30 or nineteen thirtieths. The probability of the event not happening is therefore equal to 19 out of 30.