Tree Diagrams

• The Counting Principle says that if one experiment can be performed in m ways and another can be performed in n ways, the the two experiments, in that order, can be performed in m×n ways.
• We will use this for experiments involving two actions
  • Drawing two cards from a deck
  • Rolling a die twice
  • Flipping a coin twice.
• In the case of drawing a card
  • with replacement means the card will be drawn and then replaced. It could be drawn again.
  • without replacement means the card will be drawn and set aside, it can not be drawn again.
• The sample space is the universal set, the set of all results.
  • For some repeated experiments, this is sometimes difficult to explore
• Tree Diagrams allow us to systematically explore the sample space for small sample spaces.
• The probability of an event happening at least once
  • P(event happening at least once) = 1-P(event does not happen)
  • This is useful in some applications.
• Do some problems.