Lecture 22 Section 7.1 – 7.4.1 Wed, Oct 20, 2004 Probability Lecture 22 Section 7.1 – 7.4.1 Wed, Oct 20, 2004

Random Outcomes To have a random outcome, we must have a procedure in which at least one step is left to chance. Select a student and see what is grade was on Test #1. Wherein lies the randomness? Sample space or outcome space – the set of all possible outcomes of the procedure.

Random Outcomes The various possible outcomes may be equally likely, but they do not have to be. Toss a coin. Heads or tails. Look out the window. Hurricane or no hurricane. It depends on whether you live in Florida.

Example: Toss 2 Coins Toss two coins and observe how each coin lands. Draw a tree diagram:

Example: Toss 2 Coins Toss two coins and observe how each coin lands. Draw a tree diagram: 1st coin H T

Example: Toss 2 Coins Toss two coins and observe how each coin lands. Draw a tree diagram: 2nd coin 1st coin H H T T

Example: Toss 2 Coins Toss two coins and observe how each coin lands. Draw a tree diagram: 2nd coin 1st coin H H T H T T

Example: Toss 2 Coins Toss two coins and observe how each coin lands. Draw a tree diagram: Sample Space 2nd coin 1st coin H HH H T HT H TH T T TT

Example: Toss 2 Coins The sample space is the set {HH, HT, TH, TT}.

Events Event – a collection of possible outcomes. Therefore, it is a subset of the sample space. We say that the event occurs if the actual outcome is among those included in the event. Otherwise, the event does not occur.

Events A Venn diagram is a convenient way to draw an event. Draw a rectangle that represents the sample space. Represent events as ovals within the rectangle. The ovals should overlap if the events have outcomes in common.

Example Toss two coins. Event A = exactly one coin is heads. Event B = the first coin is heads. S A B HT HH TH TT

Let’s Do It! Let’s do it! 7.7, p. 390 – Expressing Events. Let’s do it! 7.8, p. 391 – Favor or Oppose.