# 11.4.1. Calculating Probability

In a school celebration, the probability that the governor attends is 0.81, and that of the general director of education attends is 0.75, while the probability that both of them attend is 0.61. Find the probability that the general director of education ONLY attends.

• A0.14
• B0.2
• C0.95
• D0.05

### Example

In a school celebration, the probability that the governor attends is 0.81, and that of the general director of education attends is 0.75, while the probability that both of them attend is 0.61. Find the probability that the general director of education ONLY attends.

### Solution

In this case, event is the governor attending the school celebration, and event is the general director of education attending. 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 . Use this fact to solve for .

Thus, the probability that only the general director of education attends is 0.14.

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