How to utilize the rules of probability
In probability, we have some rules that become very useful when visualization gets too cumbersome. These rules help us calculate compound probabilities with ease.
The addition rule
The addition rule is used to calculate the probability of either/or events. To calculate P(A ∪ B), or P(A or B), we use the following formula:
The first part of the formula (P(A) + P(B)) helps us get the union of the two events; we have to add together the area of the circles in the universe. But why the subtraction of P(A and B)? This is because when we add the two circles, we are adding the area of intersection twice, as shown in the following diagram:
Figure 5.7 – Adding the probabilities of two events and being careful not to double count their intersection
See how both the red circles include the intersection of A and B? So, when we add them, we need to subtract just one of them to account for this, leaving...
