# 9.8.1. Operations on Events

Upon rolling an irregular die, the probability of getting the numbers , and 5 are equal, and that of getting the number 6 is three times the probability of getting the number 1. Calculate the probability of getting an odd prime number.

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### Example

Upon rolling an irregular die, the probability of getting the numbers , and 5 are equal, and that of getting the number 6 is three times the probability of getting the number 1. Calculate the probability of getting an odd prime number.

### Solution

In this case, events , , , , and are getting the numbers 1, 2, 3, 4, and 5, respectively, and event is getting the number 6. Suppose the probability of each of the events , , , , and is . The probability of event would then be .

Since events , , , , , and are mutually exclusive, and they make up the sample space, the sum of their probabilities must be equal to 1. First, use this fact to find the value of as follows:

The odd prime numbers are 3 and 5, which are represented by events and . Also, the notation refers to the probability of either event or event occurring. If and are two mutually exclusive events, then . Now use this fact to determine as follows:

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