STATISTICS AND PROBABILITY

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1 STATISTICS AND PROBABILITY MTH Scored Activity 3 Due Date:... Student Identification Name:... Address: Tel.: Score:... /100 December

2 MTH STATISTICS AND PROBABILITY This scored activity has been produced by the Société de formation à distance des commissions scolaires du Québec. Production Team (French Version) Project Coordinator: Project Coordinator (initial version): Author: Content Revisor: Pedagogical Revisor: Linguistic Revisor: Desktop Publishing: Graphic Design: Ronald Côté (SOFAD) Jean-Paul Groleau (SOFAD) Alain Malouin Jean-Paul Groleau Jean-Paul Groleau Johanne St-Martin P.P.I. inc. Serge Mercier Production Team (English Version) Project Coordinator: Translator: Content Revisor: Typesetting: Proof Reading: Jean-Simon Labrecue (SOFAD) Valerie Vucko (i-edit) Rhonda Sherwood Aalia Persaud Lorraine Brown Claudia Fulviis Despite the following statement, SOFAD authorizes all adult education centres that use the corresponding learning guide to reproduce this scored activity. SOFAD All rights for translation and adaptation, in whole or in part, reserved for all countries. Any reproduction by mechanical or electronic means, including microreproduction, is forbidden without the written permission of a duly authorized representative of the Société de formation à distance des commissions scolaires du Québec. 2 SOFAD

3 SCORED ACTIVITY 3 Scored Activity 3 covers Situations 7 to 9 in the Statistics and Probability learning guide. You must complete this activity and promptly submit it to your tutor along with any accompanying documents. Most education centres reuire students to have an average of 60% or more in order to take the final examination. Instructions Complete the Student Identification section. Carefully read each uestion before answering. Write your answers in the space provided, showing the details of your work if applicable. The total points for each uestion are indicated in parentheses to the left of the uestion number. The use of the calculator is permitted. SOFAD 3

4 MTH STATISTICS AND PROBABILITY Scored Activity 3 Points (20) 1. A lecturer has to give a talk on global warming. He has to leave before dawn because the conference is being held in a city that s a four-hour drive from his home. Unfortunately, there s a power failure and he has to choose his clothes in total darkness. He has 5 shirts in the exact same style: 1 blue (Bl), 1 grey (G), 1 beige (Be), 1 yellow (Y) and 1 orange (O). He also has to choose a pair of pants. He has three pairs: 1 black (bk), 1 grey (g) and 1 blue (bl). a) Build a tree diagram showing the set of possible outcomes. b) Represent the outcome of his outfit consisting of a grey shirt and grey pants. c) Use the tree diagram obtained in a) to represent the sample space for this series of experiments as ordered pairs. 4 SOFAD

5 SCORED ACTIVITY 3 d) How many possible outcomes are there for this series of random experiments? e) Represent event E, chooses the blue shirt, as a set of ordered pairs. f) How many different ways are there of choosing the orange shirt? (20) 2. While waiting for your driver s licence to be renewed, you head down to the building s cafeteria to buy a coffee. You can choose between a black coffee (Bl) and brown coffee (Br). You can have it with milk (M) or cream (C) and add white sugar (Ws), brown sugar (Bs) or sugar substitute (Ss). a) Build a tree diagram showing the set of possible outcomes. SOFAD 5

6 MTH STATISTICS AND PROBABILITY b) Use this diagram to represent the sample space as a set of ordered triples. c) Represent event E, having a black coffee with cream, as a set of ordered triples. d) Represent event F, having a coffee with brown sugar, as a set of ordered triples. e) Are E and F euiprobable events? f) How many different ways are there of having a coffee with cream and white sugar? (10) 3. A deck contains 52 cards: 26 red cards (13 hearts and 13 diamonds) and 26 black cards (13 clubs and 13 spades.) a) What is the probability of getting a spade? b) Express this probability as a percentage. c) Calculate the probability of getting a black card. d) Are you more likely to get a spade than a club? Justify your answer. e) Is event B, getting a black card, a certain, uncertain or probable event? 6 SOFAD

7 SCORED ACTIVITY 3 (10) 4. Determine whether the following random experiments are made up of dependent or independent events. a) We roll a die two times and note each outcome. b) One bag contains 5 red balls and 7 green balls; another bag contains 6 yellow balls and 6 black balls. We draw a ball from each bag and keep it. c) We roll two dice at the same time and note the sum of both dice. d) A bag contains 10 white balls of the same size. We draw a ball and put it aside. We then draw a second from the remaining 9 balls. e) We take the 12 face cards from a deck and put them face-down on table: the four kings, the four ueens and the four jacks. We draw a card, keep it and then draw another. SOFAD 7

8 MTH STATISTICS AND PROBABILITY (10) 5. Determine whether the two events described in each situation below are compatible, incompatible or complementary. a) We draw a card from a deck of 52 cards. Event A: getting a spade. Event B: getting a red card. b) We roll a 6-sided die. Event C: getting an even number. Event D: getting a number that s a multiple of 2. c) We draw a ball from a box containing 15 red balls, 7 black balls and 8 green balls. Event E: the ball is red. Event F: the ball is black or green. d) We draw a ball from a box containing 25 balls numbered from 1 to 25. Event G: the number is a multiple of 3. Event H: the number is a divisor of 24. e) We draw a letter from a hat containing the 26 letters of the alphabet. Event I: the letter is a vowel. Event J: the letter is one of the letters in the word documentary. 8 SOFAD

9 SCORED ACTIVITY 3 (10) 6. Determine whether the following probabilities correspond to theoretical or experimental probabilities. a) The probability of having a defective part on an assembly line. b) The probability that your brother-in-law is elected the mayor of your town in the next election. c) The probability of getting a sum of 18 after rolling a die 3 times. d) The probability of drawing an ace from a deck of cards. e) The probability that the class representative is a boy if the class has 17 girls and 10 boys. SOFAD 9

10 MTH STATISTICS AND PROBABILITY (20) 7. To get to work, a motorist has to cross two sets of traffic lights that operate independently. The lights are green half of the time, red a third of the time and yellow a sixth of the time. a) Build a tree diagram showing the set of possible outcomes. b) Calculate the probability that the motorist gets the same colour light at both intersections. c) Calculate the probability that the motorist gets at least one green light. d) Calculate the probability that the motorist gets one yellow or red light. e) Calculate the probability that the motorist gets at least one yellow or green light. 10 SOFAD

11 SCORED ACTIVITY 3 Review of Operational Competencies What is an operational competency? An operational competence is not limited to one specific subject, but is useful in all subjects. For example, the competency Adopts effective work methods is learned at different stages in all subjects. Although the acuisition of this type of competency is not the focus of any particular course, it is closely related to subject-specific competencies (mathematics, science, English, history, etc.), which reuire you to use this operational competency to various degrees without you even realizing it. There are several operational competencies. This course develops the following two: Communicates and Thinks Logically. Communicates With respect to the learning situations you have just completed, indicate your ability to interpret and convey the following information. Form of Communication Information Yes Somewhat No Symbolic Language - S - (a, b) and (a, b, c) - A = {(a, b), (c, d)} - B = {(a, b, c), (d, e, f), (g, h, i)} - A Vocabulary - Sample space - Probability - Event - Tree diagram - Ordered pair - Ordered triple - Set of ordered pairs - Set of ordered triples - Random experiment - Euiprobable - Certain event - Uncertain event - Probable event - Dependent event - Independent event - Compatible event - Incompatible event - Complementary event SOFAD 11

12 MTH STATISTICS AND PROBABILITY Calculations - Calculate a probability - Calculate a probability as a percentage - Calculate freuencies - Calculate relative freuencies Procedure - Build a tree diagram - Build a probability tree diagram Thinks Logically With respect to the learning situations that you have just completed, indicate your ability to perform the following operations. Operation Yes Somewhat No - Determine the probabilities of events - Use the rule of addition - Use the rule of multiplication - Determine the probabilities of events using complementary events 12 SOFAD

13 SCORED ACTIVITY 3 Student s uestions SOFAD 13

14 MTH STATISTICS AND PROBABILITY Tutor s comments 14 SOFAD

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