11.4.1. Calculating Probability

If the success probability of a student in physics is 0.85, in mathematics is 0.8, and in both subjects is 0.71, find his success probability in at least one of the two subjects.

• A0.94
• B0.14
• C0.09
• D0.85

Example

If the success probability of a student in physics is 0.85, in mathematics is 0.8, and in both subjects is 0.71, find his success probability in at least one of the two subjects.

Solution

In this case, event is the student's success in physics, and event is the student's success in mathematics. The notation refers to the probability of either event or event occurring, or both.

In other words, the notation refers to the probability of at least one of the events occurring. Since and are two non-mutually exclusive events, then , where the notation refers to the probability of events and occurring together. Use this fact to find .

Thus, the probability of the student's success in at least one of the two subjects is 0.94.

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