Conditional Probability and Independence

• Probability The conditional probability of A given B is

  

  Conditional probability reduces the sample space we have to work with.

• Two events are independent if . That is, knowing that event B occurred gives us no additional information on the probability that event A occurs.
• If , then A and B are dependent.

EXAMPLE: Let S be a deck of 52 cards (4 suits, 13 cards per suit), A be the event that a king is drawn, and B be the event that a spade suit ( ) is drawn.

Then

Thus, A and B are independent.

NOTE: From conditional probability, we can get the following relationship: