11.4.1. Calculating Probability

In the hiring process of a company, a person has to pass two exams; theoretical and practical. The probability of success in the theoretical exam is 0.53, in the practical exam is 0.74, and in both is 0.36. If a person applies for the first time, find his probability of success in at least one of the two exams.

• A0.91
• B0.17
• C0.38
• D0.53

Example

In the hiring process of a company, a person has to pass two exams; theoretical and practical. The probability of success in the theoretical exam is 0.53, in the practical exam is 0.74, and in both is 0.36. If a person applies for the first time, find his probability of success in at least one of the two exams.

Solution

In this case, event is the student's success in the theoretical exam, and event is the student's success in the practical exam. 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 exams is 0.91.

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