Section 4.1 Classical Probability HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.

Probability experiment – any process in which the result is random in nature. Outcome – each individual result that is possible for a given experiment. Sample space – the set of all possible outcomes for a given experiment. Event – a subset of the sample space. Probability, Randomness, and Uncertainty 4.1 Classical Probability HAWKES LEARNING SYSTEMS math courseware specialists Definitions:

Consider an experiment in which a coin is tossed and then a 6-sided die is rolled. Sample space and events: HAWKES LEARNING SYSTEMS math courseware specialists Probability, Randomness, and Uncertainty 4.1 Classical Probability Solution: a.Each outcome consists of a coin toss and a die roll. b.Choosing the members of the sample space which fit the event “tossing a tail then rolling an odd number” gives: {T1, T3, T5} a.List the sample space for the experiment. b.List the outcomes in the event “tossing a tail then rolling an odd number”.

Three methods for calculating the probability: HAWKES LEARNING SYSTEMS math courseware specialists Probability, Randomness, and Uncertainty 4.1 Classical Probability 1.Subjective – an educated guess regarding the chance that an event will occur. 2.Empirical – if all outcomes are based on experiment. 3.Classical – if all outcomes are equally likely.

Rounding probabilities: HAWKES LEARNING SYSTEMS math courseware specialists Probability, Randomness, and Uncertainty 4.1 Classical Probability 1.Give the exact fraction. 2.Round to three decimal places. 3.If the probability is extremely small, it is permissible to round the decimal to the first nonzero digit.

a.The probability of selecting the queen of spades out of a standard deck of cards. Classical b.An economist predicts a 20% chance that technology stocks will decrease in value over the next year. Subjective c.A police officer wishes to know the probability that a driver, chosen at random, will be driving under the influence of alcohol on a Friday night. At a roadblock, he records the number of drivers and the number of drivers driving with more than the legal blood alcohol limit. He determines that the probability is 3%. Empirical Determine whether each of the following probabilities is subjective, empirical, or classical: HAWKES LEARNING SYSTEMS math courseware specialists Probability, Randomness, and Uncertainty 4.1 Classical Probability

A large jar contains more marbles than you are willing to count. Instead, you draw some coins at random, replacing each coin before the next draw. You record the picks in the following table: Calculate the probability: HAWKES LEARNING SYSTEMS math courseware specialists Probability, Randomness, and Uncertainty 4.1 Classical Probability a.What is the probability that on your next draw you will obtain a blue marble? b.What is the probability that on your next draw you will obtain a yellow marble? RedBlueGreenYellowPurple