Everything Maths Grade 10

1.As a real number between 0 and 1. For example 0,75.

2.As a percentage. For example 0,75 can be written as 75%.

3.As a fraction. For example 0,75 can also be written as^34.

We note the following about probabilities:

• A probability of 0 means that an event will never occur.


• A probability of 1 means that an event will always occur.


• A probability of 0,5 means that an event will occur half the time, or 1 time out of every 2.

When all of the possible outcomes of an experiment have an equal chance of occurring, we can compute
the exact theoretical probability of an event. The probability of an event is the ratio between the number of
outcomes in the event set and the number of possible outcomes in the sample space.

P(E) =

n(E)

n(S)

VISIT:

The following video shows an example of calculating the theoretical probabilities of an event.

See video:2GVXatwww.everythingmaths.co.za

Worked example 1: Theoretical probabilities

QUESTION

What is the theoretical probability of each of the events in the first two of our three experiments?

SOLUTION

Step 1: Write down the value ofn(S)

Experiment 1 (coin):n(S) = 2

Experiment 2 (dice):n(S) = 36

Step 2: Write down the size of the event set

Experiment 1:n(E) = 1

Experiment 2:n(E) = 5

Step 3: Compute the theoretical probability

Experiment 1:

P(E) =

n(E)

n(S)

=

1

2

=0,5

Experiment 2:

P(E) =

n(E)

n(S)

=

5

36

=0,13 8 _

Note that we do not consider the theoretical probability of the third experiment. The third experiment is
different from the first two in an important way, namely that all possible outcomes (all final scores) are not

Chapter 14. Probability 473