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Geometry: Statistics 12.1 A probability experiment is an action or trial that has varying results Any possible result of a probability experiment represents an ____________ of the experiment. outcome The sample space of a probability experiment is the set of all possible outcomes Example: Determine the sample space in each situation below. You flip a coin 3 times and record the number of heads You flip a coin 3 times and record the outcome You flip a coin and roll a 6-sided die. I t would certainly be nice to know in advance how many outcomes we should expect in our sample space. Multiplication Principle: If we can do one task n1 number of ways and a second task n2 number of ways, then both n1 n2 ways. tasks together can be done in _______ Example: Find the number of possible outcomes in the sample space. Do not list them. Flip 8 coins b) flip 2 coins and roll a 6-sided die An event is a collection of one or more outcomes The probability of an event is a measure of the liklihood, or chance, the event will occur Probability is always a number between _____ 0 and _____ 1 and can be expressed as a fraction, decimal or percent. Number of outcomes in the event Total number of outcomes P(A) Example: A student taking a quiz guesses at the answers to four true-false questions. What is the probability of the students guessing exactly 2 correct answers? Example: Two 4-sided dice are rolled. What is the probability of getting a sum of 6? all outcomes that are not in A A 1 1 - P(A) Example: Consider rolling two 6-sided dice. Find the following probabilities. P(sum is not 6) b) P(sum is less than or equal to 9) A geometric probability is found by calculating a ratio of lengths, areas or volumes Example: You throw a dart at the board shown at the right. Your dart is equally likely to hit anywhere inside the square board. Find P(getting 10 points) Find P(getting 0 points)