Conditional Probability

• If we know part of the outcome of an experiment, we can modify the probability of an event based on this knowledge.
• Conditional probability is the probability of an event E₂ occurring given that knowledge that event E₁ has (or will have) occurred.
• Written P(E₂|E₁)
  • Read : probability of event 2 given event 1
  • The second set is the set we know the result is an element of. (E₁)
• P(E₂|E₁) = n(E₁ ∩ E₂)/n(E₁)
• A card is drawn from a standard deck, find the probability that it is a king given that it is a red face card.
  • E₁ is the card is a red face card.
  • E₂ is the card is a king.
  • n(E₁) = 6
  • n(E₁ ∩ E₂) = 2
  • Note some kings are not counted (the two black kings)
  • Not all cards are counted, only red face cards.
  • So P(king | red face card) = 1/3
• Do some problems page 751