Conditional probability

1
Conditional probability

• Probability of an event E, given that an event F
  has occurred is called the conditional
  probability of E given F, and is written as
  P(EF).

2
Formula for Conditional Probability

• P(EF)P(E?F)/P(F), if P(F)?0
• P(E?F) P(F).P(EF)
• OR
• P(E?F) P(E). P(FE)

3
Independent Events

• If the probability of event E does not change
  even though the event F has occurred, then we say
  that the events E and F are independent events.
  If E and F are independent events we have the
  following properties
• P(E) P(EF)
• P(F) P(FE)
• P(E?F) P(E).P(F)
• P((E?F)G) P(EG).P(FG), given G has occurred