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If the probability that a student passes an exam is 39 percent, what is the probability that the student fails?
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As there are only two possibilities in this scenario, the student could either pass or fail, they are the complements of each other.
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We know that the probability of any complementary event, denoted 𝐴 bar, is equal to one minus the probability of 𝐴.
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When dealing with percentages, the one is equal to 100 percent.
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As the probability of the student passing is 39 percent, the probability of the student failing will be 100 percent minus 39 percent.
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This is the same as saying that the student does not pass the exam and is equal to 61 percent.
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We could also write this answer as a fraction or a decimal.
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As percentages are out of 100, this can be written as a fraction as 61 out of 100 or sixty-one one hundredths.
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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.
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The probability that the student fails the exam is 61 percent, 61 out of 100, or 0.61.
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An alternative method here would be to convert 39 percent into the fraction thirty-nine one hundredths or the decimal 0.39 first.
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We could then subtract either of these from one to calculate the complement, which is equal to sixty-one one hundredths or 0.61.