Ryan rolls a fair six-sided die
numbered from one to six. Part a) Using a cross, mark on the
probability scale the probability of rolling an even number.
A probability scale is used to show
the chance or likelihood of an event occurring. Events that are impossible have a
probability of zero and events that are certain to happen have a probability of
one. Other events are placed on the
scale according to the probability of them occurring.
In part a of this question, we were
asked about the probability of rolling an even number on a fair six-sided die, which
has faces numbered from one to six. The keyword in this question is
“fair,” which means that the die has an equal probability or chance of landing on
each face. And therefore, the outcomes of one,
two, three, four, five, and six are all equally likely to occur.
There are three even numbers: two,
four, and six. And as each of these numbers are
equally likely, this means that the probability of scoring a two, a four, or a six
is three out of six or three-sixths. This fraction can be cancelled down
by dividing both the numerator and denominator by three to give one over two or
We can, therefore, put this cross
in the very center of our probability scale, at a probability of one-half.
Now, let’s look at the second part
of this question.
Part b) says, “Using a cross, mark
on the probability scale the probability of rolling a number less than four.” So we have the same setup as
before, which means the possible outcomes are the numbers one, two, three, four,
five, and six all with an equal chance of occurring. The numbers which are less than
four so that strictly less than four, not including four itself are one, two, and
So again, we have three out of six
possible outcomes, which gives a fraction of three over six, which can be simplified
to one-half. The cross for part b also goes in
the very center of the probability scale.