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.
