MYP Standard Mathematics Combined-event Probability Notes

Combined-Event Probability

1. Combined-event probability is about finding the chance that two or more events happen together, or that at least one of them happens.
2. In this topic you will use set notation, Venn diagrams, and tree diagrams, which we covered earlier, to represent situations and calculate probabilities clearly.

The Addition Rule Avoids Double Counting

1. Suppose you are given two events $A$ and $B$.
2. When you add $P(A)$ and $P(B)$, the overlap $A\cap B$ gets counted twice (once in $A$ and once in $B$).
3. The addition rule fixes that: for any events $A$ and $B$,
   $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
4. If $A$ and $B$ are mutually exclusive, then $P(A\cap B)=0$ and the rule simplifies to: $$P(A\cup B)=P(A)+P(B)$$

Independent Events And The Multiplication Idea

Sometimes one event does not affect the probability of the other.

A common example is rolling a die twice: the first roll does not influence the second roll.