# 11.4.1. Calculating Probability

If and are two events of a random experiment, where , , and , find the probability of occurrence of one of the two events at most.

• A0.8
• B0.6
• C0.5
• D0.3

### Example

If and are two events of a random experiment, where , , and , find the probability of occurrence of one of the two events at most.

### Solution

Since and are complementary, the sum of their probabilities is equal to 1. First, use this fact to find the probability of .

The notation refers to the probability of either event or event occurring, or both. If and are two non-mutually exclusive events, then ,

where the notation refers to the probability of events and occurring together.

Now use this fact to determine .

Since and are complementary, the sum of their probabilities is equal to 1. Next, use this fact to find the probability of .

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. Thus, the probability of the occurrence of at most one of the events is 0.8.

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