# 11.4.1. Calculating Probability

If and are two events in a sample space of a random experiment, where , and the probability of occurrence of one of them at most is 0.86, while at least it is 0.87, determine the probability of occurrence of only one of them.

• A0.73
• B0.01
• C0.14
• D0.13

### Example

If and are two events in a sample space of a random experiment, where , and the probability of occurrence of one of them at most is 0.86, while at least it is 0.87, determine the probability of occurrence of only one of them.

### Solution

The notation refers to the probability of events and occurring together, so the notation refers to the probability of events and not occurring together. In other words, the notation refers to the probability of the occurrence of at most one of the events. Since and are complementary, the sum of their probabilities is equal to 1. First, use this fact to find

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. This means that the probability of occurrence of only one of the events is the difference of and Now find the difference of and as follows:

Thus, the probability of occurrence of only one of the events is 0.73.

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