Question Video: Determining the Probability of the Complement of a Given Event Mathematics • Third Year of Preparatory School

Video Transcript

If the probability that a student passes in mathematics is 0.7, what is the probability that the student fails?

In this question, we will begin by recalling the formula to calculate the probability of the complement of an event. The probability of the complement of event 𝐴, written 𝐴 bar or 𝐴 prime, is equal to one minus the probability of 𝐴. In this question, we are told the probability that a student passes mathematics is 0.7. Since there are only two options here, either the student passes or fails, the probability that the student fails is equal to one minus the probability that they pass. This is therefore equal to one minus 0.7, which is equal to 0.3.

The probability that a student fails mathematics is 0.3.