= Basic Probability Notes Basics of Probability Probability Definitions Experiment – activity under consideration Outcomes – observable results from the experiment Trials – repetition of the experiment Relative frequency – this is the probability of a certain outcome (like temperature, or an exam grade) Experimental Probability ­ The probability of what happens during trials Theoretical Probability ­ The probability of what should happen during trials Basics of Probability Sample Space – all your possible outcomes What is your sample space for the following: flipping a coin once flipping a coin twice rolling a die rolling 2 dice Event – subset of your sample space Example: rolling a 3 with one die, flipping a coin and getting heads Probability How to find probability: # of ways an event can occur Total number of outcomes Experimental Probability Probability = Theoretical = # times an event occurs Total number of trials Example A college has an enrollment of 1210 students. The number in each class is as shown. Class # of students Example Allen has a bucket of chips. In this bucket there are 5 red, 6 yellow and 2 black chips. Find each probability. P(red) P(white) P(not black) Freshmen 420 Sophomore 315 Junior 260 Senior 215 Total 1210 What is the probability that a student selected at random will be a Freshman? Sophomore? Junior? Senior?

Experimental is not always the same as theoretical. Basic Probability Notes Example Sample space for a standard deck of cards A card is randomly selected from a standard deck of cards. Find each probability. P(Face Card) P(red seven) P(heart) EX: Flipping a coin What is the probability of it landing on heads? What if you flipped the coin 3 times? How many possible out comes are there? Example Sample space for rolling a pair of dice A pair of dice is rolled. Find each probability. P( both die are even) P(sum is 10) P(roll doubles) P(sum is 13) P(sum is > 2) Rules of Probability P(A) is always between 0 and 1 If P(A)=0, then P(B) is 100 If P(B)=0 then P(A) IS 100 Theoretical vs. Experimental Probability Theoretical Probability: Experimental (Empirical) Probability: Theoretical vs. Experimental Probability continued: Law of Large Numbers Experimental is not always the same as theoretical. After a large number of trials, experimental probability should get closer to the theoretical probability.