Question 1

What is the difference between 'mutually exclusive' and 'independent' events?

Accepted Answer

Mutually exclusive events cannot happen at the same time ($P(A \cap B) = 0$). Independent events can happen at the same time, but the occurrence of one does not change the probability of the other ($P(A \cap B) = P(A) 	imes P(B)$). Think of rolling a die: 'getting a 1' and 'getting a 6' are mutually exclusive. Tossing a coin twice: 'getting a head on the first toss' and 'getting a head on the second toss' are independent.

Question 2

When should I use a tree diagram versus a Venn diagram?

Accepted Answer

Venn diagrams are excellent for visualising the relationships (union, intersection, complement) between two or three events in a single experiment, especially for problems involving counts or the addition rule. Tree diagrams are best for multi-stage experiments where outcomes are sequential and often conditional, like drawing items without replacement. They help you systematically list all possible outcomes and calculate their probabilities by multiplying along the branches.

Question 3

How do I know if I should add or multiply probabilities?

Accepted Answer

You ADD probabilities when you are considering alternative outcomes (Event A *OR* Event B). This corresponds to the union of events, $P(A \cup B)$. You MULTIPLY probabilities when you are considering a sequence of events (Event A *AND THEN* Event B). This corresponds to the intersection of events, $P(A \cap B)$. Be careful to use the correct multiplication rule (for independent vs. dependent events).

Probability

What you need to know

The Rules of Chance