Mathematics SSE

7.0. Introductory Activity

A woman applying the family planning program considers the assumption that 

one boy or one girl can be born at each delivery. If she wishes to have 3 children 

including two girls and one boy, she knows that this is a case among other cases 

which can happen for the 3 children she can have. Discuss all these cases and 

deduce the chance the woman has for having a girl at the first and the second 

delivery and a boy at the third delivery.

Activity 7.

Probability is the chance that something will happen. 

The concept of probability can be illustrated in the context of a game of 52 playing 

cards. In a park of deck of 52 playing cards, cards are divided into four suits of 13 

cards each. If a player selects a card at random (by simple random sampling), then 

each card has the same chance or same probability of being selected.

When a coin is tossed, it may show Head (H- face with logos) or Tail (T-face with 

another symbol).

We cannot say beforehand whether it will show head up or tail up. That depends on 

chance. The same, a card drawn from a well shuffled pack of 52 cards can be red or 

black. That depends on chance. Such phenomena are called probabilistic. The theory 

of probability is concerned with this type of phenomena. 

Probability is a concept which numerically measures the degree of uncertainty and 

therefore, of certainty of occurrence of events. 

In most sampling situations we are generally not concerned with 

sampling a specific individual but instead we concern ourselves with the 

probability of sampling certain types of individuals. 

Random experiments and Events

A random experiment is an experiment whose outcome cannot be predicted or 

determined in advance.

Example of experiments: 

– Tossing a coin,

– Throwing a dice

– Selecting a card from a pack of paying cards, etc. 

In all these cases there are a number of possible results (outcomes) which can occur 

but there is an uncertainty as to which one of them will actually occur. 

Each performance in a random experiment is called a trial. The result of a trial in 

a random experiment is called an outcome, an elementary event, or a sample point. 

The totality of all possible outcome (or sample points) of a random experiment

constitutes the sample space which is denoted by Ω . Sample space may be discrete 

or continuous. 

Discrete sample space: 

• Firstly, the number of possible outcomes is finite. 

• Secondly, the number of possible outcomes is countably infinite, which means 

that there is an infinite number of possible outcomes, but the outcomes can be