Addition Rule for Non-Mutually Exclusive Events

When do we use the addition rule?

If we want to calculate the probability of event A occurring or event B occurring, taking into account that they are mutually exclusive, we use the addition rule.

Formula:

P(A or B) = P(A) + P(B) - P(A and B), where

• P(A or B) - the probability of event A occurring or event B occurring,
• P(A) - the probability of event A occurring
• P(B) - the probability of event B occurring
• P(A and B) - the probability of events A and B occurring simultaneously

Task example:

In the class, there are 18 boys and 12 girls; 15 people have dark hair (3 girls and 12 boys). What is the probability of randomly choosing a girl or a dark-haired student?

1. P(girl) = 12/30 = 0.4 = 40%
2. P(dark-haired student) = 15/30 = 0.5 = 50%
3. P(girl and dark-haired student) = 3/15 = 20%
4. P(girl or dark-haired student) =P(girl) + P(dark-haired student) - P(girl and dark-haired student) = 40% + 50% - 20%= 70%.