Example
1
.
For the experiment ‘roll a fair die’, ±nd the probabilities of:
A
,
the event that an even number is rolled,
B
, the event that an odd number is
rolled, and
C
, the event that either a 1 or a 2 is rolled.
Solution:
If an experiment consists of rolling a fair die, then the possible
outcomes are the numbers which may be rolled. We see that
S
=
{
1
,
2
,
3
,
4
,
5
,
6
}
with

S

= 6
and we have
A: roll an even number
⇒
A
=
{
2
,
4
,
6
}
so

A

= 3
B: roll an odd number
⇒
B
=
{
1
,
3
,
5
}
so

B

= 3
C: roll a 1 or a 2
⇒
C
=
{
1
,
2
}
so

C

= 2
Since each number is equally likely to come up when we roll a fair die, we
have:
prob
(
A
) =

A


S

=
3
6
=
1
2
prob
(
B
) =

B


S

=
3
6
=
1
2
prob
(
C
) =

C


S

=
2
6
=
1
3
When the various outcomes of an experiment are
not
equally likely to oc
cur, then we ±nd the probability of an event by adding up the probabilities
of the various outcomes contained in the event.
Notice:
This is e²ectively
what we have done for equally likely outcomes, too.
Example
2
.
An urn contains 1 yellow ball, 2 red balls, 3 blue balls and 4
green balls. One ball is drawn from the urn at random. Find the probability
that either a yellow or a blue ball is drawn.
Solution:
We can de±ne the outcomes of this experiment as the colour of
the ball drawn. Letting
Y
,
R
,
B
and
G
denote yellow, red, blue and green,
respectively, we have
S
=
{
Y,R,B,G
}
.