Pencil highlighter GP notebook calculator textbook assignment Marvin
Pencil, highlighter, GP notebook, calculator, textbook, assignment Marvin owns 2 green shirts and 3 white shirts. He also owns 3 pairs of blue jeans and 1 pair of black jeans. Make a tree diagram illustrating the possibilities of picking one 1 shirt and 1 pair of jeans each morning. Start the tree by showing the branches for choosing a shirt, and then continue the tree with the branches for choosing a pair of jeans. Include all labels. total:
Marvin owns 2 green shirts and 3 white shirts. He also owns 3 pairs of blue jeans and 1 pair of black jeans. Make a tree diagram illustrating the possibilities of picking one 1 shirt and 1 pair of jeans each morning. Start the tree by showing the branches for choosing a shirt, and then continue the tree with the branches for choosing a pair of jeans. +1 +1 five branches Shirts +1 labels G +1 G W W W Jeans B B B Bk B Bk +2 four branches each +2 labels total:
PM – 11 Penny Ante’s teacher has a box with pencils and erasers in it. There are currently THREE YELLOW, ONE BLUE, and TWO RED PENCILS in it along with ONE YELLOW and TWO RED ERASERS. She has just bet her friend a dime to his dollar that she could walk by the teacher’s desk and, without looking, grab a blue pencil and a red eraser from the box. Should her friend accept this challenge? a) Make a tree diagram or an area model of all the possibilities, using subscripts to account for the colors for which there is more than one pencil or eraser. b) Use the tree or list to find the probability of Penny snatching the blue –red combination. c) Should Penny’s friend take the bet? Why or why not?
PM – 11 Let’s make a tree diagram: Yp Yp Yp B Rp Rp Era ser s Pencils Y Re Re Y Re Re b) Use the tree or list to find the probability of Penny snatching the blue–red combination. P(blue pencil, red eraser) =
PM – 11 Here is a possible area model. P(blue pencil, red eraser) = Erasers Y Pencils Re Re Yp Yp Y Yp Re Yp Yp Y Yp Re B BY B Re Rp Rp Y Rp R e B Re
PM – 11 c) Should Penny’s friend take the bet? Why or why not? P(blue pencil, red eraser) = Her friend probably should not take the bet since Penny’s probability of success is and her pay off ratio is. Penny has a slightly better than “fair” expectation since: >1
PM – 12 From your tree diagram or area model in the preceding problem it should now be easy to find the probability for each of the six color combinations of a pencil and eraser that Marty named. Make a list of the correct probabilities for Gerri. For example, P(B, Re) = P(Rp, Re) = P(Yp, Y) = P(Yp, R) = Pencils P(B, Y) = P(Rp, Y) = Erasers Y Re Re Yp Yp Y Yp Re Yp Yp Y Yp Re B BY B Re Rp Rp Y Rp R e B Re
PM 13 – 16, 18 Worksheet Directions: Roll two dice 36 times and record the sum. Instead of actually rolling 2 dice, we are going to simulate the activity using a graphing calculator. On your calculator, we first need to make sure that each calculator does not give the same probabilities, so do the following: MATH PRB 5: rand. Int( 1 , 6 , 2 )
PM 13 – 16, 18 Worksheet Directions: Roll two dice 36 times and record the sum. Instead of actually rolling 2 dice, we are going to simulate the activity using a graphing calculator. On your calculator, select: MATH PRB 5: rand. Int( 1 , 6 , 2 ) When finished, the main calculator screen will display: rand. Int(1, 6, 2) {3 6} {2 5} This function means that the calculator will “randomly” select two integers between 1 and 6. Hit ENTER on the calculator. Add the 2 numbers. Continue to hit ENTER until you have filled in the table.
Find the empirical probabilities (what happened): P(2) = ____ P(5) = ____ P(8) = ____ P(11) = ____ P(3) = ____ P(6) = ____ P(9) = ____ P(12) = ____ P(4) = ____ P(7) = ____ P(10) = ____ What should the denominator be for each probability? 36
Second Die Directions: Fill in the table with the sum of the two dice. Compute theoretical probabilities (what was expected to happen). First Die 1 2 3 4 5 6 1 2 2 3 4 5 6 7 3 4 4 5 6 7 5 6 6 7 7 8 P(2) = ____ P(8) = ____ 8 P(3) = ____ P(9) = ____ 8 9 P(4) = ____ P(10) = ____ 8 9 10 11 P(5) = ____ P(11) = ____ 9 10 11 12 P(6) = ____ P(12) = ____ P(7) = ____
OR problems – problems in which you are asked Probability "____" or another thing might to calculate the probability that one thing ____ add happen. Generally, we ____ the probabilities together. Examples: If a 6 -sided die is rolled, compute the probabilities: P (1 or 4) = P (even # or 5) = P (2, 3, or 4) = AND problems – problems in which you are asked Probability "_____" and another thing to calculate the probability that one thing _____ same ______. time happen at the ______ Examples: If a 6 -sided die is rolled, compute the probabilities: P (rolling even # and 6) = P (rolling 2 and 5) =
Directions: Determine the following probabilities based on your table. First Die 1) P (sum = 2 or 4) = 3) P (sum ≥ 5) = 4) P (sum is not 5) = 5) P (both dice = 2) = 6) P (at least 1 die = 2) = Second Die 2) P (sum > 5) = 1 2 3 4 5 6 7 8 9 4 5 6 7 8 9 10 11 12
Directions: Determine the following probabilities based on your table. First Die 7) P (exactly 1 die = 2) = 9) P (sum < 2) = 10) P (sum at most 10) = Second Die 8) P (sum < 13) = 11) P (5 < sum < 8) = 12) P (sum > 8 and sum < 5) = 1 2 3 4 5 6 7 8 9 4 5 6 7 8 9 10 11 12
Directions: Make a double-bar graph to compare your empirical probabilities to theoretical probabilities. Use a separate sheet of graph paper! Example: Empirical Probability Theoretical This is due by FRIDAY!!! etc 0 1 2 3 etc sum Your empirical graph will be different than others, however, your theoretical graph should be the same for everyone.
Finish the assignment: Double Bar graph, PM 17, 19 – 25
Old Slides
Recall the Quadratic Formula: There is a special name for the expression under the radical sign. discriminant because it b 2 – 4 ac is called the ______ “discriminates” the type of zeros of the quadratic function. 2 complex roots and the * If b 2 – 4 ac < 0, then there are ________, no x–intercepts. graph of y = ax 2 + bx + c has ___ one real rational root and the * If b 2 – 4 ac = 0, then there is __________, graph of y = ax 2 + bx + c has one ___ x–intercept. perfect square, then there are * If b 2 – 4 ac > 0, and is a _______ two real rational roots and the graph of __________, 2 x–intercepts. y = ax 2 + bx + c has ___ perfect square, then there are * If b 2 – 4 ac > 0, and is not a _______ two real irrational roots and the graph ___________, 2 x–intercepts. of y = ax 2 + bx + c has ___
Practice: For each quadratic, determine the discriminant and the type of zeros. 1) a=4 b=4 c=1 1 real rational root 2) a = – 2 b = 1 c = 3 This is a perfect square! 2 real rational roots
Practice: For each quadratic, determine the discriminant and the type of zeros. 3) a=2 b=1 c=3 2 complex roots 4) a = 3 b = – 1 c = – 5 2 real irrational roots
Practice: For each quadratic, determine the discriminant and the type of zeros. 5) a = – 1 b = 2 c = – 1 1 real rational root 6) a=2 b=1 c=5 2 complex roots
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