# Question Video: Determining the Probability of the Union of Two Events Mathematics

The probability that a student passes their physics exam is 0.85. The probability that they pass their mathematics exam is 0.8. The probability that they pass both exams is 0.71. What is the probability that the student passes at least one of the two exams?

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### Video Transcript

The probability that a student passes their physics exam is 0.85. The probability that they pass their mathematics exam is 0.8. The probability that they pass both exams is 0.71. What is the probability that the student passes at least one of the two exams?

We will begin by letting 𝐴 be the event that a student passes physics. This means that the probability of event 𝐴 is 0.85. We will let 𝐵 be the event that a student passes mathematics. This means that the probability of event 𝐵 is 0.8. We are told that the probability that a student passes both exams is 0.71. This is the intersection of events 𝐴 and 𝐵. The probability of 𝐴 intersection 𝐵 is 0.71.

We have been asked to calculate the probability that a student passes at least one of the two exams. This is the probability of 𝐴 union 𝐵, the probability that they pass physics or mathematics or both. The addition rule of probability states that the probability of 𝐴 union 𝐵 is equal to the probability of 𝐴 plus the probability of 𝐵 minus the probability of 𝐴 intersection 𝐵. Substituting our values from this question, we have the probability of 𝐴 union 𝐵 is equal to 0.85 plus 0.8 minus 0.71. This is equal to 0.94. The probability that a student passes at least one of the two exams is 0.94, or 94 percent.