# Video: Finding the Probability of a Difference of Two Events given the Probability of Each Event as well as Their Intersection

The probability that a student passes their physics exam is 0.71. The probability that they pass their mathematics exam is 0.81. The probability that they pass both exams is 0.68. What is the probability that the student only passes their mathematics exam?

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### Video Transcript

The probability that a student passes their physics exam is 0.71. The probability that they pass their mathematics exam is 0.81. The probability that they pass both exams is 0.68. What is the probability that the student only passes their mathematics exam?

If we let the blue circle represent the probability that students pass their math exam, we’ll let the yellow circle be physics. The probability that students pass their mathematics exam is 0.81. The probability they pass their physics exam is 0.71. The probability that they pass both exams is 0.68. The probability that students pass their math exam is equal to the probability that they pass only their math exam plus the probability that they pass the math and physics exam.

We know the probability that they pass both is 0.68. We also know the overall probability of passing the math exam is 0.81. Which means to find the probability that they only pass math, we subtract the probability that they pass math and physics from the probability of passing math. When we do that, we get 0.13. So, we say the probability that students only pass their math exam is 0.13. This is because the 0.13 plus the 0.68 equals the original 0.81 probability that they would pass the math exam.

The probability that students only pass the math exam is 0.13.