Question Video: Determining the Theoretical Probability of an Event | Nagwa Question Video: Determining the Theoretical Probability of an Event | Nagwa

# Question Video: Determining the Theoretical Probability of an Event Mathematics • Second Year of Secondary School

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A school club contained 32 boys and 26 girls. If a student is selected at random from the club, what is the probability that the student is a girl?

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### Video Transcript

A school club contains 32 boys and 26 girls. If a student is selected at random from the club, what is the probability that the student is a girl?

We begin by recalling that the probability of an event is the chance or likelihood of it occurring. This probability can be written as a fraction, where the numerator is the number of successful outcomes and the denominator is the total number of outcomes. In this question, we are selecting a student from a school club which contains 32 boys and 26 girls, and we wish to calculate the probability that the student is a girl. As there are 26 girls, the numerator of our fraction will be 26. 32 plus 26 is equal to 58. This means that there are 58 students in the club in total, and therefore the denominator is 58.

The probability of selecting a girl from the school club is 26 out of 58. This fraction can be simplified. And as the numerator and denominator are even, they are divisible by two. 26 divided by two or a half of 26 is 13 and 58 divided by two is 29. The probability that the selected student is a girl is 13 out of 29 or thirteen twenty-ninths.

Whilst it is not required in this question, it follows that the probability the selected student is a boy is 16 out of 29. This is because the two probabilities are the complement of one another and must sum to one.

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