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MATH1342 Collin College LAB 4 Spring 2015 NAME: _________________ Instructor: Daryl Rupp DUE DATE: WE - 2/16/15 SCC - 2/17/15 PART I: 1. Given a single die with FOUR sides (instead of 6 – NOT 6 sides) where each side will have a number: one side numbered 1, one side numbered 2, one side numbered 3 and one side numbered 4. The die will be made of hard rubber so it will bounce before coming to rest. The number on the side that lands “down” will be the outcome. a. What will be the sample space of the experiment of rolling one die? b. What is P(3)? ________ P(5)? ____ P(even number)? ________ P(1 x 4 )? ______ P(x < 4)? _______ c. Now consider the experiment of rolling 2 of the four sided dice and the outcome is the total of the two “down” sides. The sample space will be {2, 3, 4, 5, 6, 7, 8}. Find in the number of ways each of the sample space outcomes can be obtained and fill in the table below including the probability of each outcome and the total of all probabilities: Outcome 2 3 4 5 6 7 8 Total # of Ways P(Outcome) d. In problem 1c. above, if one event is rolling a 6 and another event is rolling an 8, then are these two events Mutually Exclusive or Not Mutually Exclusive PART II: Some plain M&M’s and some peanut M&M’s are mixed in a bag. The following is the number of each color and type of M&M found in the bag of 360 M&M’s. Use the table for Part II and Part III. Red Orange Yellow Green Blue Brown TOTAL Plain Peanut Total 50 35 15 75 52 23 72 50 22 51 35 16 33 23 10 79 55 24 250 110 360 Suppose you reach into the bag and randomly select one M&M. Calculate the following probabilities of selecting one M&M that is (described). Show your calculations and round your answers to 4 decimals. 1. P (Red) = 2. P (Peanut) = 3. P (Blue) = 4. P (Blue and Plain) = 5. P (Orange and Brown) = 6. P(Orange or Brown) = 7. P (Not Yellow) = 8. P (Blue or Plain) = 9. P (Brown give that the one you picked is Plain) = PART III: Use the same table of data from Part II. Suppose you reach into the sample bag and randomly select THREE M&M’s. Calculate the following probabilities (with and without replacement). Show your calculations and round your final answers to 4 decimals. 1. The probability that the first M&M is Red, the second M&M is Yellow, and the third M&M is Blue. (with replacement) 2. The probability that the first M&M is Red, the second M&M is Yellow, and the third M&M is Blue. (without replacement) 3. The probability that all three M&M’s are Blue. (with replacement) 4. The probability that all three M&M’s are Blue. (without replacement) 5. Would it be unusual for all three M&M’s to be blue if the sampling is done without replacement? Justify your answer using a complete sentence and proper grammar. PART IV: The following problems use the counting techniques methods used in Section 5.5. Show your calculations and the answers will be in whole numbers. 1. If a three character code is to be made from the letters {a, b, c, d, e} and the letters can be reused, how many different codes can be made? 2. Same as 1. without reusing any letter? 3. If you are selecting a meal from a menu and you have 4 choices of appetizers, 2 choices of salads, 5 choices of main courses, 6 choices of desserts, how many different meals do you have to select from (assuming you had to have one selection from each course)? 4. Given that 52% of a city (of more than 1,000,000 people) are in favor of a bond issue and 4 people who favored it are to be selected from the voters in the city, what is the probability that the first 4 people selected would favor the issue? 5. A lottery consists of selecting 3 single digits from the 10 digits (0 through 9), without replacement and order matter. How many different 3 digit numbers can be made? 6. A lottery consists of selecting 3 single digits from the 10 digits (0 through 9), without replacement and order does not matter. How many different 3 digit numbers can be made?