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The probability that a student passes their physics exam is 0.85.
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The probability that they pass their mathematics exam is 0.8.
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The probability that they pass both exams is 0.71.
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What is the probability that the student passes at least one of the two exams?
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We will begin by letting 𝐴 be the event that a student passes physics.
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This means that the probability of event 𝐴 is 0.85.
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We will let 𝐵 be the event that a student passes mathematics.
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This means that the probability of event 𝐵 is 0.8.
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We are told that the probability that a student passes both exams is 0.71.
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This is the intersection of events 𝐴 and 𝐵.
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The probability of 𝐴 intersection 𝐵 is 0.71.
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We have been asked to calculate the probability that a student passes at least one of the two exams.
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This is the probability of 𝐴 union 𝐵, the probability that they pass physics or mathematics or both.
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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.
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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.
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This is equal to 0.94.
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The probability that a student passes at least one of the two exams is 0.94, or 94 percent.