# Video: Determining the Probability of Complement of an Event

A class in a school contains 38 students. At the end of the school year 28 of the students passed mathematics, 32 passed science, and 26 passed both science and mathematics. If a student is chosen at random from the class, what is the probability that they failed science.

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### Video Transcript

A class in a school contains 38 students. At the end of the school year, 28 of the students passed mathematics, 32 passed science, and 26 passed both science and mathematics. If a student is chosen at random from the class, what is the probability that they failed science?

The probability that they failed science is the exact same thing as the probability of not passing science, and if the probability of passing science would be 32 out of 38, because 32 students passed science out of the total 38 students in the class.

So if 32 out of the 38 passed, how many didn’t pass? Well it would be the remainder of the students in the class. Of 32 passed, how many students are left? There would be six students left. Therefore, six out of the 38 did not pass science, which means they failed science, and we can reduce this fraction by dividing the numerator and denominator by two and getting three nineteenths.

So if a student is chosen at random from the class, the probability that they failed science will be three nineteenths.