Total possible outcomes are required for theoretical
probability calculations. A table shows the possibilities.
Explore the total possible outcomes of the following pairs
of events.
One Coin
Complete a chart to show
all of the possible outcomes of flipping one coin.
Compare it to the table below.
Event:
Coin Flip
H
T
number of possible outcomes = 2
One
Six-sided Die
The following shows the possible outcomes when you toss a die.
Roll the die several times until you see the
six different numbers displayed on the die
Event:
Die Toss
1
2
3
4
5
6
number of possible outcomes = 6
Theoretical Probability of a
Single Event
The theoretical probability of the event
is the fraction:
# ways the event can occur
total possible outcomes
Coin
Flip
When you flip a coin, there are only 2 sides
- heads and tails. The theoretical probability for
each is:
P(H) = 1/2 = 0.5
P(T) = 1/2 = 0.5
Spin
Wheel
When a spinner has 5 equal sized sectors of
green, red, yellow, and blue, the theoretical
probability for each is:
P(red) = 1/5 = 0.20
P(orange) = 1/5 = 0.20
P(yellow) = 1/5 = 0.20
P(green) = 1/5 = 0.20
P(blue) = 1/5 = 0.20
Toss
Die
When you toss a 6-sided dice, there are 6 sides.
The theoretical probability (to
the nearest hundredth) for each is:
P(1) = 1/6 = 0.17
P(2) = 1/6 = 0.17
P(3) = 1/6 = 0.17
P(4) = 1/6 = 0.17
P(5) = 1/6 = 0.17
P(6) = 1/6 = 0.17
Theoretical probability does not change. In the first examples
each individual event had the same probability. The next
example shows events with different probabilities.
Experimental Probability
Coin
Flip
The experimental probability for equally
likely events is the fraction:
# favourable outcomes
total outcomes
If you toss a coin 50 times and you end up with 20 heads and
30 tails, the experimental probability is:
P(H) = 20/50 = 0.4
P(T) = 30/50 = 0.6
Theoretical experiment changes from experiment
to experiment. If the experiment is fair, the theoretical
and experimental probability should be very similar if a
large number of trials are made. Try flipping a coin
yourself. Flip it 50 times and record the numbers of
heads and tails. Divide your totals by 50 to get the
experimental probability. Coin toss simulations are
available on the internet. Try these:
