L06 - Independent and Dependent Events

Independent and Dependent Events

Learning Intention

• I can check for independent events.

Independent Events

• Events are independent when the outcome of one event does not change the probability of obtaining the other events.
• Let’s take the example of two events.

Two Independent Events (Formulae)

When two events are independent, then the following are true:

• $P(A|B)=P(A)$
• $P(B|A)=P(B)$
• $P(A\cap B)=P(A)\times P(B)$

Dependent Events

• Dependents events occur when the probability of one outcome does change the probability of obtaining the other events.

Multi-Stage Experiment

• Multi-stage experiments such as two-step experiments have certain conditions.
• If the experiment is with replacement, then the successive events are independent.
• If the experiment is without replacement, then the success events are dependent.