# 11.4.1. Calculating Probability

Given that and are two events in a sample space of a random experiment, where , , and , determine .

• A0.85
• B0.21
• C0.3
• D0.94

### Example

Given that and are two events in a sample space of a random experiment, where , , and , determine .

### Solution

The notation refers to the probability of the occurrence of and the non-occurrence of . Also, the notation refers to the probability of events and occurring together. For this reason, is equal to the sum of and . First, solve for in terms of as follows:

The notation refers to the probability of the occurrence of and the non-occurrence of . Another way to write it is . For this reason, is equal to the sum of and . Now use substitution to again solve for in terms of .

Next, use substitution to solve for .

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

De Morgan's Second Law states that , where the notation means the non-occurrence of or the non-occurrence of , or both. Since , it follows that .

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