Tree Diagrams

• The Counting Principle states that if an experiment can be performed in m ways and a second experiment can be performed in n ways, then both experiments in that order can be performed in mxn ways.
• I will sometimes call this the fundamental counting principle because.
• Assume we toss a coin then roll a die.
• A Tree diagram allows us to explore the sample space or all possible outcomes.
• P(an event happening at least once) = 1- P(event does not happen)
• If an experiment is performed repeatedly on the same items that are removable, it can be done
  • with replacement: that means the item selected is returned and can be selected again.
    • The number of outcomes do not change.
  • without replacement: or it is not returned and the outcomes are reduced by 1.
• Do some problem 667 on.