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

If the probability of an event occurring is 13/36, what is the probability that it does not occur?

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Video Transcript

If the probability of an event occurring is 13 out of 36, what is the probability that it does not occur?

An event not occurring is known as the complement of an event. This is denoted 𝐴 bar or 𝐴 prime. And the probability of the complement is equal to one minus the probability of 𝐴. This is because the sum of the probability an event occurs and the probability it does not occur equal one.

If we let 𝐴 be the event in this question, then the probability of 𝐴 is equal to 13 out of 36. The probability of 𝐴 bar is therefore equal to one minus 13 out of 36. This is the same as 36 out of 36 minus 13 out of 36. As the denominators are the same, we simply subtract the numerators, giving us 23 out of 36. This is the probability that the event does not occur.

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