# 9.8.1. Operations on Events

The table below shows the data of 245 people who went to an exhibition. If one of them is randomly chosen, find the probability that the chosen visitor is a woman or foreigner.

GenderNationalForeignerTotal
Man5984143
Woman9012102
Total14996245
• A
• B
• C
• D

### Example

The table below shows the data of 245 people who went to an exhibition. If one of them is randomly chosen, find the probability that the chosen visitor is a woman or foreigner.

GenderNationalForeignerTotal
Man5984143
Woman9012102
Total14996245

### Solution

The probability of event occurring is equal to the number of favorable outcomes divided by the total number of possible outcomes in the sample space, . In this case, event is choosing a woman. Find the probability of event as follows:

The probability of event occurring is equal to the number of favorable outcomes divided by the total number of possible outcomes in the sample space, . In this case, event is choosing a foreigner. Find the probability of event as follows:

The notation refers to the probability of either event or event occurring, or both. If A and are two non-mutually exclusive events, then , where the notation refers to the probability of events and occurring together. Next, use this fact to determine .

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