Video: Determining the Theoretical Probability of an Event

A class contains 6 boys and 21 girls. If a pupil is selected at random, what is the probability they are a girl?

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Video Transcript

A class contains six boys and 21 girls. If a pupil is selected at random, what is the probability they are a girl?

The probability of an event happening can be written as a fraction where the numerator, or top number, is the number of successful outcomes and the denominator, or bottom number, is the number of possible outcomes.

In this case, the total number of pupils is 27 as six plus 21 equals 27. Therefore, the number of possible outcomes are also 27. We want to find the probability that the selected pupil is a girl.

Well in this question, there are 21 girls. Therefore, the number of successful outcomes is 21. We can therefore say that the probability of selecting a girl at random is twenty-one twenty-sevenths or 21 out of 27.

This fraction can be simplified or cancelled by dividing the numerator and denominator by three. 21 divided by three is equal to seven. And 27 divided by three is equal to nine.

This means that the probability of selecting a girl at random from a class containing six boys and 21 girls is seven out of nine or seven-ninths.

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