Part
One: Probability
Probability
Rules: A Fair, Six-sided Die
Begin
with a die with six sides: 1,2,3,4,5,6. Suppose that this die is fair - that
each face has an equal chance of showing in tosses of the die.
From
earlier discussions, this table shouldn't require much explanation:
|
Face
Value |
Probability
(Proportion) |
Probability
(Percentage) |
Odds
Statement |
|
1 |
1/6 |
16.67% |
1:6 |
|
2 |
1/6 |
16.67% |
1:6 |
|
3 |
1/6 |
16.67% |
1:6 |
|
4 |
1/6 |
16.67% |
1:6 |
|
5 |
1/6 |
16.67% |
1:6 |
|
6 |
1/6 |
16.67% |
1:6 |
|
Total |
6/6 |
100%** |
6:6 |
Basic
Events
In
repeated tosses of our die, the most basic possible outcomes are the faces
themselves - the individual face values are the basic events. Each basic event
has the same probability - (1/6).
The
Additive Rule
Define
the event EVEN as follows: "an even face (2,4,6) shows". Then the
probability of the event EVEN can be computed as :
Pr{EVEN}=Pr{
exactly one of 2 or 4 or 6 shows } = Pr{2 shows} + Pr{4 shows} + Pr{6 shows}
Pr{EVEN}=
(1/6) + (1/6) + (1/6) = 3/6 = .50 or 50%
Complementary
Rule
Define
the event 2PLUS as "a face greater than or equal to 2 shows". Then
its complementary event is Not2PLUS is "a face strictly less than 2
shows", and can be computed as :
Pr{not2PLUS}
= Pr{ 1 shows } = 1/6. Then compute the probability for the event 2PLUS as :
Pr{2PLUS}
= 1 - Pr{not2PLUS} = 1 - (1/6) = 5/6 .