# 11.4.1. Calculating Probability

A class contains 25 boys and 13 girls, where 5 boys and 4 girls wear glasses. If one student was selected randomly from this class, find the probability that the student does NOT wear glasses.

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### Example

A class contains 25 boys and 13 girls, where 5 boys and 4 girls wear glasses. If one student was selected randomly from this class, find the probability that the student does NOT wear glasses.

### 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 selecting a boy who wears glasses. 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 selecting a girl who wears glasses. Now find the probability of event .

The notation refers to the probability of either event or event occurring.

Since and are two mutually exclusive events, then . Next, use this fact to determine the probability of .

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

Thus, the probability of selecting a student who does not wear glasses is .

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