# Video: Determining the Probability of Complement of an Event

If the probability that a student passes an exam is 39%, what is the probability that the student fails?

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### Video Transcript

If the probability that a student passes an exam is 39 percent, what is the probability that the student fails?

As there are only two possibilities in this scenario, the student could either pass or fail, they are the complements of each other. We know that the probability of any complementary event, denoted 𝐴 bar, is equal to one minus the probability of 𝐴. When dealing with percentages, the one is equal to 100 percent. As the probability of the student passing is 39 percent, the probability of the student failing will be 100 percent minus 39 percent. This is the same as saying that the student does not pass the exam and is equal to 61 percent.

We could also write this answer as a fraction or a decimal. As percentages are out of 100, this can be written as a fraction as 61 out of 100 or sixty-one one hundredths. As a decimal, this is equal to 0.61 as the line in a fraction means divide and 61 divided by 100 is 0.61. The probability that the student fails the exam is 61 percent, 61 out of 100, or 0.61.

An alternative method here would be to convert 39 percent into the fraction thirty-nine one hundredths or the decimal 0.39 first. We could then subtract either of these from one to calculate the complement, which is equal to sixty-one one hundredths or 0.61.