2.7 Independent Events and Unions of Events

Calculate probabilities for independent events and for the union of two events.

• Events A and B are independent if and only if knowing whether event A has occurred (or will occur) does not change the probability that event B will occur. When events A and B are independent, then P AB PA(|)=() , P BA PB(|)=() , and P AB PA PB∩() = () . () .
• The probability that event A or event B (or both) will occur is the probability of A union B. The probability of the union is defined as P (AB∪ .)
• P ABunion () = P PP AB AB() + () - () intersect , or P AB PPPA B AB∪() = () + () -∩() .