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UNIT 5: PROBABILITY Basic Probability Sample Space Set of all possible outcomes for a chance experiment. Example: Rolling a Die Probability Model • It is a description of some chance process that consists of two parts • A sample space (S) • A probability for each outcome Tree Diagram A technique for listing the outcomes in a sample space. It contains branches showing what can happen on different trials. Draw diagram of all possibilities of test performance on three True/False questions. Draw the tree diagram for winning the best 2 out of 3 games. Imagine rolling two fair, six-sided dice – one that is red and one that is green. Give a probability model for this chance process. Event • It is a subset of the sample space. • It is usually designated by capital letters, like A, B, C, and so on. Consider flipping 2 coins A = both tails B = at least one head Find P(A) P(B) Basic Rules of Probability – (don’t write yet) • Complement • Mutually Exclusive (Disjoint) • Two events are mutually exclusive (disjoint) if they have no outcomes in common and so can never occur together. Basic Probability Rules • Find the probability: • Rolling a 5 • Choosing a girl in this class • Drawing a king Two marbles are pulled from a bag holding one red, one white, one blue, and two green marbles. A={the blue marble is drawn} B={a green marble is drawn} Distance learning courses are rapidly gaining popularity among college students. Randomly select an undergraduate student who is taking a distance-learning course for credit, and record the student’s age. Here is the probability model. Age Group (Yr): Probability: 18 to 23 24 to 29 30 to 39 40 or over 0.57 0.17 0.14 0.12 • Show that this is a legitimate probability model. • Find the probability that the chosen student is not in the traditional college age group (18 to 23). Choose an American adult at random. Define two events: A = the person has a cholesterol level of 240 mg per deciliter of blood (mg/dl) or above (high cholesterol). B = the person has a cholesterol level of 200 to 239 mg/dl (bordering high cholesterol) According to the American Heart Association, P(A) = 0.16 and the P(B) = 0.29. • Explain why events A and B are mutually exclusive. • What is P(A and B)? • What is P(A or B)? • If C is the event that ther person chosen has normal cholesterol (below 200 mg/dl), what is P(C)? Homework