A school club has 25 boys and 13
girls. Of the members in the club, five of
the boys and four of the girls wear glasses. If a club member is chosen at
random, what is the probability that they do not wear glasses?
There are lots of ways of
approaching this problem. One way would be to set up a
two-way table. The two-way table can be drawn as
shown. We are told in the question that
there are 25 boys in the club. There are 13 girls in the club. As 25 plus 13 is equal to 38, there
are 38 members altogether. We are also told that five of the
boys wear glasses. This means that 20 of the boys did
not wear glasses as 25 minus five is 20. Four of the girls in the club wear
glasses. This means that nine do not. The total number of students that
wear glasses is nine as five plus four equals nine. 20 plus nine is equal to 29. Therefore, there are 20 students in
the club who do not wear glasses.
We recall that probability can be
written as a fraction where the numerator is the number of successful outcomes and
the denominator the number of possible outcomes. We need to work out the probability
that a student does not wear glasses. There are 29 club members that do
not wear glasses. Therefore, our numerator will be
29. The total number of students in the
club is 38. Therefore, the denominator is
38. We can therefore conclude that the
probability that a club member does not wear glasses is 29 out of 38.