Probability 1: Theoretical Probability, Sample Space and Venn Diagrams

The Foundation of Probability

Probability quantifies how likely an event is to occur. In MYP Year 5 Standard, you work with theoretical probability — calculating probabilities based on equally likely outcomes rather than from collected data.

Theoretical Probability

The probability of an event A is defined as:

P(A) = number of favourable outcomes / total number of outcomes

Probabilities always lie between 0 (impossible) and 1 (certain), inclusive. Expressing answers as fractions, decimals, or percentages are all acceptable — check what the question asks for.

Sample Space

The sample space is the complete set of all possible outcomes. Listing the sample space systematically is the first step in many probability problems.

For a single fair die, the sample space is {1, 2, 3, 4, 5, 6}. For two coins, it is {HH, HT, TH, TT}. Sample space diagrams (grids) are a useful tool when two events are involved.

Venn Diagrams

Venn diagrams represent events as overlapping circles within a rectangle (the universal set). They are particularly useful for problems involving:

• Events that share outcomes (intersection)
• Events where all outcomes in either set are counted (union)
• Outcomes outside both events (complement)

You need to be able to complete a Venn diagram from given information and read probabilities directly from it.

Common Mistakes

• Forgetting that probabilities in a sample space must sum to 1
• Placing values in the wrong region of a Venn diagram (particularly the intersection)
• Treating the complement as impossible rather than calculating 1 − P(A)