Video Transcript
A class has 45 students. The probability of choosing at
random a student whose age is 10 or less is two-thirds. How many students in the class are
11 or older?
There are two possibilities when
selecting a student in this question. They could be aged 10 or less, or
11 or older. These are known as complementary
events. We know that the probability of any
complementary event, 𝐴 bar, occurring is equal to one minus the probability of 𝐴,
the event itself occurring. We are told in the question that
the probability of choosing a student whose age is 10 or less is equal to
two-thirds. This means that the probability of
selecting a student who is not 10 or less is equal to one-third as one minus
two-thirds is one-third. This is the same as saying the
probability of selecting a student who is 11 or older is one-third. One-third of the 45 students are
aged 11 or older.
We can calculate this by
multiplying one-third by 45. Multiplying any number by one-third
is the same as dividing the number by three. We know that four divided by three
is equal to one remainder one. 15 divided by three is equal to
five. As 45 divided by three is equal to
15, one-third multiplied by 45 is also 15. There are 15 students in the class
who are aged 11 or older. An alternative method here would be
to calculate two-thirds of 45 first. This is the number of students who
are aged 10 or less. As one-third multiplied by 45 is
15, two-thirds multiplied by 45 is 30. There are 30 students in the class
whose age is 10 or less.
As 30 students are aged 10 or less,
we can subtract this from 45 to calculate the number of students that are 11 or
older. Once again, this gives us an answer
of 15 students.
