Probability 2: Combined Events, AND/OR Rules and Probability Trees
Learn combined events, AND/OR probability rules and probability trees for IB MYP Year 5 Standard Maths. Clear steps with common exam mistakes highlighted.
Taking Probability Further
Having built your foundation in Probability 1, this topic focuses on events that involve more than one outcome — known as combined events. You will use formal rules and diagrams to calculate probabilities in more complex situations.
The AND and OR Rules
OR Rule (Addition Rule)
For mutually exclusive events (events that cannot happen at the same time):
P(A or B) = P(A) + P(B)
If events are not mutually exclusive, you must subtract the overlap: P(A or B) = P(A) + P(B) − P(A and B).
AND Rule (Multiplication Rule for Independent Events)
For independent events (where the outcome of one does not affect the other):
P(A and B) = P(A) × P(B)
Independence is a key assumption here — always check whether the context supports it.
Probability Trees
Probability trees are structured diagrams that map out sequences of events. Each branch shows one possible outcome and its probability. The probability of a specific sequence is found by multiplying along the branches.
Using Probability Trees
- All probabilities on branches from a single node must sum to 1
- Calculate the probability of each outcome path by multiplying along it
- Add probabilities for paths that satisfy the condition you are calculating
Common Mistakes
- Adding probabilities along branches instead of multiplying
- Using the simple AND rule when events are not independent
- Not listing all possible paths when solving for combined outcomes
Criterion A and D Relevance
Tree diagrams test procedural accuracy (Criterion A) but also appear in real-life contexts — medical testing, quality control, sports outcomes — which connects to Criterion D. Always interpret your final probability in context.