Pencil, highlighter, GP notebook, calculator, textbook, assignment U10D2 Have out: Bellwork: 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 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 G W W W +1 B Bk B Bk B Bk B Bk Jeans B B B Bk +2 four branches each total: +2 labels

Should Penny’s friend take the bet? Why or why not? 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? 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. Use the tree or list to find the probability of Penny snatching the blue–red combination. Should Penny’s friend take the bet? Why or why not?

Let’s make a tree diagram: PM – 11 Let’s make a tree diagram: Pencils  Yp Yp Yp B Rp Rp Erasers Y Re Re Y Re Re Y Re Re Y Re Re 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) =

Here is a possible area model. PM – 11 Here is a possible area model. P(blue pencil, red eraser) = Erasers Y Re Re Yp Yp Y Yp Re Yp Re Yp Yp Y Yp Re Yp Re Yp Yp Y Yp Re Yp Re Pencils B B Y B Re B Re Rp Rp Y Rp Re Rp Re Rp Rp Y Rp Re Rp Re

Penny has a slightly better than “fair” expectation since: 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, Erasers P(B, Re) = P(Rp, Re) = Y Re Re Yp Yp Y Yp Re Yp Re P(Yp, Y) = Yp Yp Y Yp Re Yp Re P(Yp, R) = Yp Yp Y Yp Re Yp Re Pencils B B Y B Re B Re P(B, Y) = Rp Rp Y Rp Re Rp Re P(Rp, Y) = Rp Rp Y Rp Re Rp Re

Take out: 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: randInt( 1 , 6 , 2 )

Take out: 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: randInt( 1 , 6 , 2 ) When finished, the main calculator screen will display: This function means that the calculator will “randomly” select two integers between 1 and 6. randInt(1,6,2) {3 6} {2 5} Hit on the calculator. Add the 2 numbers. Continue to hit until you have filled in the table. ENTER ENTER

Find the empirical probabilities (what happened): What should the denominator be for each probability? 36

Directions: Fill in the table with the sum of the two dice Directions: Fill in the table with the sum of the two dice. Compute the theoretical probabilities (what was expected to happen). First Die 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 P(2) = ____ P(3) = ____ P(4) = ____ P(5) = ____ P(6) = ____ P(7) = ____ P(8) = ____ P(9) = ____ P(10) = ____ P(11) = ____ P(12) = ____ Second Die

Examples: If a 6-sided die is rolled, compute the probabilities: Probability "____" problems – problems in which you are asked to calculate the probability that one thing ____ another thing might happen. Generally, we ________ the probabilities together. OR or add Examples: If a 6-sided die is rolled, compute the probabilities: P (1 or 4) = P (even # or 5) = P (2, 3, or 4) = Probability "_____" problems – problems in which you are asked to calculate the probability that one thing _____ another thing happen at the ______ ______. AND and same time 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) = 2) P (sum > 5) = 3) P (sum ≥ 5) = 4) P (sum is not 5) = 5) P (both dice = 2) = 6) P (at least 1 die = 2) = 1 2 3 4 5 6 7 8 9 10 11 12 Second Die

Directions: Determine the following probabilities based on your table. First Die 7) P (exactly 1 die = 2) = 8) P (sum < 13) = 9) P (sum < 2) = 10) P (sum at most 10) = 11) P (5 < sum < 8) = 12) P (sum > 8 and sum < 5) = 1 2 3 4 5 6 7 8 9 10 11 12 Second Die

Example: Empirical Probability Theoretical etc Directions: Make a double-bar graph to compare your empirical probabilities to the theoretical probabilities. Use a separate sheet of graph paper! Example: Empirical Probability Theoretical etc This is due by FRIDAY!!! sum 1 2 3 etc 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. b2 – 4ac is called the ____________ because it “discriminates” the type of zeros of the quadratic function. discriminant * If b2 – 4ac < 0, then there are _______________, and the graph of y = ax2 + bx + c has ___ x–intercepts. 2 complex roots no * If b2 – 4ac = 0, then there is ___________________, and the graph of y = ax2 + bx + c has ___ x–intercept. one real rational root one perfect * If b2 – 4ac > 0, and is a _______ square, then there are ____________________, and the graph of y = ax2 + bx + c has ___ x–intercepts. two real rational roots 2 perfect * If b2 – 4ac > 0, and is not a _______ square, then there are _____________________, and the graph of y = ax2 + bx + c has ___ x–intercepts. two real irrational roots 2

Practice: For each quadratic, determine the discriminant and the type of zeros. 1) 2) a = 4 b = 4 c = 1 a = –2 b = 1 c = 3 This is a perfect square! 1 real rational root 2 real rational roots

Practice: For each quadratic, determine the discriminant and the type of zeros. 3) 4) a = 2 b = 1 c = 3 a = 3 b = –1 c = –5 2 complex roots 2 real irrational roots

Practice: For each quadratic, determine the discriminant and the type of zeros. 5) 6) a = –1 b = 2 c = –1 a = 2 b = 1 c = 5 1 real rational root 2 complex roots