Basic Probability Notes Definitions Experiment activity under consideration

Basic Probability Notes Definitions Experiment – activity under consideration Basics of Probability 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 Sample Space – all your possible outcomes What is your sample space for the following: 1. flipping a coin once Probability How to find probability: 2. flipping a coin twice Theoretical 3. rolling a die Probability 4. rolling 2 dice = # of ways an event can occur Total number of outcomes Event – subset of your sample space Experimental Example: rolling a 3 with one die, flipping a coin and getting heads Probability Example # of students 420 315 260 215 1210 Total number of trials Sophomore? Junior? Allen has a bucket of chips. In this bucket there are 5 red, 6 yellow and 2 black chips. Find each probability. 1. P(red) 2. P(white) What is the probability that a student selected at random will be a Freshman? # times an event occurs Example A college has an enrollment of 1210 students. The number in each class is as shown. Class Freshmen Sophomore Junior Senior Total = Senior? 3. P(not black)

Basic Probability Notes Example EX: Flipping a coin Sample space for a standard deck of cards What is the probability of it landing on heads? What if you flipped the coin 3 times? How many possible out comes are there? A card is randomly selected from a standard deck of cards. Find each probability. 1. P(Face Card) 2. P(red seven) 3. P(heart) Example Sample space for rolling a pair of dice Rules of Probability P(A) is always between 0 and 1 is 100 P(B)=0 then P(A) IS 100 A pair of dice is rolled. Find each probability. If P(A)=0, then P(B) 1. P( both die are even) If 2. P(sum is 10) 3. P(roll doubles) 4. P(sum is 13) 5. P(sum is > 2) 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 theoretical probability.