Experiments, Outcomes and Events

1. Experiments, Outcomes and Events

2. Experiment • Describes a process that generates a set of data • Tossing of a Coin • Launching of a Missile and observing its velocity • Opinions of Voters concerning a new tax • An experiment is a situation involving chance or probability that leads to results called outcomes.

3. Trial • A single performance of an experiment is called a Trial. • The result of a trial is called an Outcome or a Sample Point. • The set of all possible outcomes of an experiment is called a Sample Space. • Subsets of a Sample Space are called Events.

4. Sample Space • Inspecting a light bulb • Rolling a dice • Asking for opinions about a new car model • An experiment consists of flipping a coin and then flipping it second time, if a head occurs. If a tail occurs on a first flip, then a die is tossed once.

5. Examples – Sample Space • The set of integers between 1 and 50 and divisible by 8 • S = { x! x2 + 4x – 5 = 0 } • Set of outcomes when a coin is tossed until a tail or three heads appear • Set of sampling items randomly until one defective item is observed.

6. Problem • Which of the following events are equal? • A = { 1, 3} • B = { x ! x is a number on the die} • C = { x ! x2 - 4x + 3 = 0 } • D = { x ! x is the number of heads when six coins are tossed }

7. Definitions • An event is a subset of a Sample Space. • The complementof an event A with respect to S is the subset of all elements of S that are not in A. • The intersection of two events A and B is the event containing all elements that are common to A and B. • The union of two events A and B is the event containing all the elements that belong to A or B or both.

8. Mutually Exclusive Events • Two events A and B or Mutually Exclusive or Disjoint, if A and B have no elements in common.

9. Problem 1 • Graph a Sample Space for the experiment: Tossing Two Coins

10. Problem 3 • Graph a Sample Space for the experiment: Rolling Two Dice

11. Problem 5 • Graph a Sample Space for the experiment: Rolling a Dice until the first six appears

12. Problem 11 • In rolling two dice, are the events: • A: Sum divisible by 3 • B: Sum divisible by 5 are mutually exclusive?

13. Problem 17 • Using Venn Diagram, graph and check De Morgan’s Law.

14. Problem • A glass jar contains 1 red, 3 green, 2 blue and 4 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of each outcome?