The Independence & Multiplication Rule

Objectives

• Identify independent events
• Use the Multiplication Rule for Independent Events
• Compute at-least probabilities

Two events E and F are independent if the occurrence of event E in a probability experiment does not affect the probability of event F. Two events are dependent if the occurrence of event E in a probability experiment affects the probability of event F.

Multiplication Rule for Independent Events

If E and F are independent events, then

P (E and F) = P(E) x P(F)

Multiplication Rule for n Independent Events

If E1, E2, E3, … and En are independent events, then

P(E1 & E2 & E3 & ... & En)
= P(E1) x P(E2)...x P(En)