Tutorial Quiz 1_Version A_Solutions

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University of Waterloo *

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135

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Mathematics

Date

Jan 9, 2024

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pdf

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9

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Instructions Marking Scheme: 1. All electronic devices are to be turned off and put away. 2. This is a closed-book quiz. 3. Answer the questions in the spaces provided. 4. Final answers to written questions should be rounded to THREE DECIMAL PLACES, or left in fraction form, where appropriate 5. Only question pages will be marked. 6. You may tear off the last page and use it for rough work. All pages will be collected at the end of the quiz. 7. Only a non-programmable, non-graphical calculator with a pink-tie or blue-goggle sticker will be allowed. No other aids are allowed. 8. DO NOT WRITE ON THIS COVER PAGE. Questions Out of 1 – 9 9 10 11 11 6 Total 26
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Part 1: Multiple Choice – Each question is worth 1 mark Please CLEARLY CIRCLE your answer selection on this page. Do NOT simply write your choice next to the question. If you do, the question will not be graded. Each question has one correct answer. Choose the best answer. 1. Even though he is not a fan of the Toronto Raptors (professional basketball team), Alex does follow the team’s progress. Alex has many friends who believe that the Raptors will definitely win a championship within the next five years. He does not believe this to be true. However, Alex does believe that there is a 40% chance that the Raptors will win a championship within the next five years. The type of probability being used here is: A) Classical probability B) Subjective probability C) Relative frequency probability • There is really no rational basis underlying this probability statement. It is essentially based on a feeling or opinion. As such, it would be an example of a subjective probability statement. 2. To determine whether the waiting time to be served is less than 7 minutes at a local restaurant, the waiting times of 300 customers were observed over a 4-hour period. It was found that 186 customers out of the 300 experienced a wait of less than 7 minutes. The manager of the restaurant declares that the probability of waiting less than 7 minutes is 186/300 = 0.62. Which definition of probability best describes the above scenario? A) Classical probability B) Subjective probability C) Relative frequency probability • The statement is based on a long series of repetitions of an experiment or process -- in this case, the observation of waiting times for a large number of customers. For this reason, the relative frequency definition is the best choice to describe the situation.
3. A fair six-sided die is to be rolled two times. Each time the die is rolled, the number of pips (dots) on the upturned face is recorded. What is the probability that number of dots will be different in each of the two rolls? Note: “Fair” implies that each face is equally likely to be observed on any roll. A) 5/6 B) 1/4 C) 1/3 D) 1/12 E) None of these • In this case: • S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), ……, (6,5), (6,6)}. • As such, we see that there are a total of 36 outcomes in the sample space. • To solve this probability, it may be easier to look at the complement. • The outcomes “the number of dots will be THE SAME in the two rolls are given by: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). There are 6 outcomes in this case. • Thus, the probability that the number of dots will be different in each of the two rolls (36 – 6)/36 = 30/36 = 5/6. 4. Consider a well shuffled standard deck of 52 playing cards. A card is drawn from the deck and its face value is observed. What is the probability that its face value is a prime number? Notes: Let Jack = 11, Queen = 12, King = 13, and Ace = 1. The face value of all other cards is equal to the number on the card. 1 is not a prime number. A) 4/13 B) 5/13 C) 6/13 D) 7/13 • There are 13 possible face values in the deck, of which 6 are primes (2, 3, 5, 7, 11, and 13). So, the probability of selecting a card with a face value that is a prime number is 6/13. Use the following information to answer the next TWO questions: Two numbers from {1, 2, 3, 4, 5, 6} are to be randomly chosen with replacement. Each number is equally likely to be chosen, and each number is recorded after each selection. 5. How many outcomes are in the sample space for this experiment? A) 6 B) 12 C) 24 D) 36 • In this case, S = {(1, 1), (1, 2), …, (1,6), (2, 1), (2, 2), …, (2,6), (3, 1), (3,2), (3,3), …(3, 6), (6,1), (6,2), …., (6, 6)}. • We see that there are a total of 36 outcomes in the sample space.
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