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1. In a survey of 30 consumers of detergents, 5 people said they are loyal to brand A, while another 5 are loyal to brand B. Five surveyed said they do not use either brands A, B, nor C, but use some other detergents not included in the survey. A total of ten consumers said they prefer brand A, and a total of 11 said they prefer brand C. Four said they are using both A and B. There were no one who used both brands B and C. Further, almost peculiarly, no one said they used A, B, and C simultaneously. a. How many person uses brand A or brand B but not brand C? b. How many person uses both brand A and brand C?

1. In a survey of 30 consumers of detergents, 5 people said they are loyal to brand A, while another 5 are loyal to brand B. Five surveyed said they do not use either brands A, B, nor C, but use some other detergents not included in the survey. A total of ten consumers said they prefer brand A, and a total of 11 said they prefer brand C. Four said they are using both A and B. There were no one who used both brands B and C. Further, almost peculiarly, no one said they used A, B, and C simultaneously. a. How many person uses brand A or brand B but not brand C? b. How many person uses both brand A and brand C?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Assessment Task: A. Sample Space, Events, Venn Diagram and Counting Sample Points 1. In a survey of 30 consumers of detergents, 5 people said they are loyal to brand A, while another 5 are loyal to brand B. Five surveyed said they do not use either brands A, B, nor C, but use some other detergents not included in the survey. A total of ten consumers said they prefer brand A, and a total of 11 said they prefer brand C. Four said they are using both A and B. There were no one who used both brands B and C. Further, almost peculiarly, no one said they used A, B, and C simultaneously. a. How many person uses brand A or brand B but not brand C? b. How many person uses both brand A and brand C? 2. Five different mathematics books, 4 different electronic books, and 2 different communication books are to be placed in a shelf with the books of the same subject together. Find the number of ways in which the books can be placed. 3. In how many ways can the letters of the word "PROBABILITIES" be arranged if the first place is to be filled with a consonant and no consonants are to be adjacent to each other? 4. Thirteen poker hands is to be taken from an ordinary deck of cards. How many ways it can contain two aces, three face cards, four cards greater than 2 but less than 5,and three cards greater than 4 but less than 10? B. Basic Probability 1. One box contains four cards numbered 1, 3, 5, and 6. Another box contains three cards numbered 2, 4, and 7. One card is drawn from each box. Find the probability that the sum is even. 2. A box contains 5 red balls and 3 yellow balls. If 4 balls, one at a time will be drawn at random from the box without replacement. What is the probability that the balls alternate in colors? 3. An ordinary die is tossed once. If a 1 appears, a ball is drawn from Urn 1. If a 2, 3 or 4 appears, a ball is drawn from Urn 2; otherwise, a ball is drawn from Urn 3. Urn 1 contains 5 white, 3 green and 2 red balls. Urn 2 contains 1 white, 6 green and 3 red balls. Urn 3 contains 3 white, 1 green and 6 red balls. What is the probability that a red ball is drawn? 4. A box of a dozen mechanical components contains 7 good components and 5 bad components. Mr. Mechanical Engineer is preparing machine design for his four projects. One component is required per machine. He randomly selects 4 components from the box. a. What is the probability that the Mr. Mechanical Engineer got at most one bad component? b. What is the probability that Mr. Mechanical Engineer will have to get components from the box again? C. Conditional Probability 1. The probability that machine A will break down on a particular day is P(A) = 1/50; similarly, for machine B, P(B) = 1/100. Assuming independence, on a particular day, what is the probability that at most one will break down? 2. A candidate runs for two political offices, A and B. He assigns 0.30 as the probability of being elected to both, 0.6 as the probability of being elected to A if he is elected to B and 0.8 as the probability of being elected to B if he is elected to A. What is the probability of being elected to A?
Transcribed Image Text:Assessment Task: A. Sample Space, Events, Venn Diagram and Counting Sample Points 1. In a survey of 30 consumers of detergents, 5 people said they are loyal to brand A, while another 5 are loyal to brand B. Five surveyed said they do not use either brands A, B, nor C, but use some other detergents not included in the survey. A total of ten consumers said they prefer brand A, and a total of 11 said they prefer brand C. Four said they are using both A and B. There were no one who used both brands B and C. Further, almost peculiarly, no one said they used A, B, and C simultaneously. a. How many person uses brand A or brand B but not brand C? b. How many person uses both brand A and brand C? 2. Five different mathematics books, 4 different electronic books, and 2 different communication books are to be placed in a shelf with the books of the same subject together. Find the number of ways in which the books can be placed. 3. In how many ways can the letters of the word "PROBABILITIES" be arranged if the first place is to be filled with a consonant and no consonants are to be adjacent to each other? 4. Thirteen poker hands is to be taken from an ordinary deck of cards. How many ways it can contain two aces, three face cards, four cards greater than 2 but less than 5,and three cards greater than 4 but less than 10? B. Basic Probability 1. One box contains four cards numbered 1, 3, 5, and 6. Another box contains three cards numbered 2, 4, and 7. One card is drawn from each box. Find the probability that the sum is even. 2. A box contains 5 red balls and 3 yellow balls. If 4 balls, one at a time will be drawn at random from the box without replacement. What is the probability that the balls alternate in colors? 3. An ordinary die is tossed once. If a 1 appears, a ball is drawn from Urn 1. If a 2, 3 or 4 appears, a ball is drawn from Urn 2; otherwise, a ball is drawn from Urn 3. Urn 1 contains 5 white, 3 green and 2 red balls. Urn 2 contains 1 white, 6 green and 3 red balls. Urn 3 contains 3 white, 1 green and 6 red balls. What is the probability that a red ball is drawn? 4. A box of a dozen mechanical components contains 7 good components and 5 bad components. Mr. Mechanical Engineer is preparing machine design for his four projects. One component is required per machine. He randomly selects 4 components from the box. a. What is the probability that the Mr. Mechanical Engineer got at most one bad component? b. What is the probability that Mr. Mechanical Engineer will have to get components from the box again? C. Conditional Probability 1. The probability that machine A will break down on a particular day is P(A) = 1/50; similarly, for machine B, P(B) = 1/100. Assuming independence, on a particular day, what is the probability that at most one will break down? 2. A candidate runs for two political offices, A and B. He assigns 0.30 as the probability of being elected to both, 0.6 as the probability of being elected to A if he is elected to B and 0.8 as the probability of being elected to B if he is elected to A. What is the probability of being elected to A?
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