Question Video: Determining the Theoretical Probability of an Event Mathematics

Video Transcript

A class has 18 boys and nine girls. What is the probability that a randomly selected student is a girl?

In this question, we’re told that there’s a class made up of 18 boys and nine girls. We need to find the probability that if we were just to pick one of these students, we would pick a girl. A really common misconception is to think that if we just picked one of these students, we’d either get a boy or a girl. We might therefore think that the probability is 50/50 or a half. However, this is incorrect. After all, if we think about it, there’s more boys than girls. Therefore, we’re more likely to pick a boy than a girl.

When we have an event like this, where we’re picking something and there’s just one outcome, in this case boy or girl, then we can apply the rule that the probability of this event is equal to the number of possible outcomes over the total number of outcomes. So in this question, because we want to find the probability of picking a girl, then the number of possible outcomes in this case would be the number of girls. The total number of outcomes would be the total number of students.

Once we’ve written the equation in the context of the question we’re working with, then we just need to fill in any values we’ve been given. We’re told that there are nine girls. But be careful because the total number of students is not 18 because that’s the number of boys. To find the total number of students, we add together the boys and the girls, giving us 27. Of course, it’s always good to simplify a fraction when we can. And nine over 27 simplifies to one-third. And so we found that the probability of picking a girl is one-third.