PROBABILITY

What is Probability? Def: The chance of an event occuring. Where is it used? –Lotteries, gambling, weather forecasting, insurance, investments, etc.

Basic Concepts Probability Experiment – A chance process that leads to well-defined results called outcomes. Examples: tossing a coin, rolling a die, drawing a card from a deck, etc.

Basic Concepts Outcome – The result of a single trial of a probability experiment Examples: Coin – Heads Dice - # 6 Card - Queen

Basic Concepts Sample Space – The set of all possible outcomes of a probability experiment. Examples: ExperimentSample Space Toss a single coinH, T Roll a die1, 2, 3, 4, 5, 6 Tossing 2 coinsHH, HT, TH, TT Selecting single card from a deck On Page 170

Basic Concepts Event – Consists of a set of outcomes of a probability experiment. An event can be a single outcome (simple event) or more than one outcome (compound event). Simple event – tossing a die Compound event – tossing a pair of dice.

Classical Probability Assumes that all outcomes in the sample space are equally likely to occur. Formula: The probability of event E occuring is given by:

Example 1: For a card drawn from an ordinary deck, find the probability of getting a queen.

Example 2: A roulette wheel has 38 spaces numbered 1 through 36, 0 and 00. Find the probability of getting these results. a)An odd number b)A number greater than 25. c)A number less than 15 not counting 0 and 00.

Example 2: Solution Sample Space = {0, 00, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}

Example 3: A card is drawn from an ordinary deck of cards. Find these probabilities: a)Of getting a jack. b)Of getting the 6 of clubs. c)Of getting a 3 or a diamond. d)Of getting a 3 and a diamond.

Basic Rules of Probability 1)The probability of an event occuring cannot be greater than 1 or less than 0. 2)Probability can be expressed as a fraction, decimal or percent. 3)The probabilities of each individual event in a sample space will always sum to 1. 4)The probability of an event occuring will always be the same as 1 – the event not occuring. (Complement Rule)

The Complement Rule P(E) = 1 – P’(E) Example: In a survey 36% of American parents use bribery to get their children to behave. If a parent is selected at random, what is the probability he/she does not use bribery? P(does not use) = 1 – P(uses) P(does not use) = =.64 or 64%