Experiments, Outcomes and Events

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.

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.

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.

Examples – Sample Space The set of integers between 1 and 50 and divisible by 8 S = { x! x 2 + 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.

Problem Which of the following events are equal? – A = { 1, 3} – B = { x ! x is a number on the die} – C = { x ! x 2 - 4x + 3 = 0 } – D = { x ! x is the number of heads when six coins are tossed }

Definitions An event is a subset of a Sample Space. The complement of 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.

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

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

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

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

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

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

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?