(a) What are the states of one standard (6-sided) die? What is the probability of each state occurring? (b) Consider a system of two standard dice. How many microstates are there? How many macrostates are there?

Q: Example 3.12. n persons are seated on n chairs at a round table. Find the probability that two…

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Q: An experiment of drawing two different dice one time, if the random variable X represents the…

A: Answer

Q: taining four P100 bills, two P200 bills, three P500 bills, and one P1,000 bill. Construct a…

A: The sample space formed is , S: 100,100,100,100,200,200,500,500,500,1000 Probability for the given…

Q: Betty has several of the standard six-sided dice that are common in many board games. If Betty rolls…

A: Note :- As per our policy, we can answer one question with three sub-parts only at a time, please…

Q: 1.) Problem : Sources of Energy Uses in the United States A breakdown of the sources of energy used…

A: a. The breakdown of sources of energy used in the United States is given.

Q: Using a fair coin and a fair six-sided dice, what is the probability of tossing tails and rolling an…

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Q: Consider a game in which six true dice are rolled. Find the probability of obtaining (a) exactly one…

A: According to the answering guidelines, we can answer only one question with three subparts and the…

Q: Example 2.4.5 What is the probability of obtaining multiples of 3, twice in a throw of 6 dice?

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Q: involving the rolling of two fair dice. Answer the following questions. (1) What is the probability…

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Q: 12. When Sue sees a bag of marbles, she grabs a handful at random. She has a bag that contains four…

A: There are total (4+3+2+1)=10 marbles in the bag.She can pick 5 marbles from 10 marbles in 10C5=252…

Q: Question involving the rolling of two fair six-sided dice. Answer the following questions. (1) What…

A: Two fair six-sided dice have been rolled. The total possible outcome is 36. The probability of an…

Q: 28. A math class consists of 25 students, 14 females, and 11 males. Three students are selected at…

A: The probability that  two females are selected, then one male is 0.145

Q: 4. Imagine you want to design a web page for your new engineering consulting firm, and you found an…

A: Hello!We are considering the number of colors as 6, according to given colors red, blue, green,…

Q: Consider two six-sided dice. a. Calculate the probability of rolling a "3" on a single die. b.…

A: Solution: 15. Suppose two dice are rolled. Then, the sample space is Number of elements in the…

Q: What real-life scenarios/industries, in your opinion, must be making/make use of the probability…

A: Probability : Probability could be a field of arithmetic that deals with numerical descriptions of…

Q: Situation A landscape gardener employs several students to help him with his work. One morning they…

A: Given: In a box, 5 left handed gloves and 8 right handed gloves are present. The objective is to…

Q: involving the rolling of two fair dice. Answer the following questions. (1) What is the probability…

A: 1) Even numbers on a die = 2,4,6 The sum can be 7 using an even number in : (2,5) , (5,2) , (4,3) ,…

Q: 1. The sum of two six-sided dice is a uniformly distributed random number.

A: Hi you have posted multiple question in one go. So as the guidelines I am obliged to answer first…

Q: Example 8.11 What is the probability of getting tail, head, and tail on three successive tosses of a…

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Q: A game consists of spinning an unbiased, five-sided spinner which can land on A, B, C, D or E, and…

A: Given information: The five sided spinner which can land on A, B, C, D or E and unbiased die are…

Q: Example 2.3.31 Two persons throw a pair of dice once each. What is the probability that the outcome…

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Q: Given chess game pieces: king queen bishop rook knight pawn Number of black pieces 1 Number of white…

A: Given problem Given that   Given chess game pieces   king queen bishop rook knight  pawn…

Q: Roulette: a Nevada roulette wheel has 38, pockets. Eighteen of them are red, eighteen of them are…

A: There is total 38 pockets, among which 18 are red, 18 are black and 2 are green.

Q: 4-) You enter a chess tournament where your probability of winning a game is 0.3 against half the…

A: Define The event W as winning a game. The event X1 as playing with type 1, P(W|X1)=0.3, since 50 of…

Q: A student body has 18 social science majors, 20 science majors, and 13 humanities majors. A…

A: Solution: Total students body= 18 social majors + 20 science majors + 13 humanities major = 51…

Q: Question 2: Axioms, interpretations and properties of probability A factory manufactures three…

A: According to the answering guidelines, we can answer only three subparts of a question and the rest…

Q: Example 2.3: Roll a pair of fair dice once and let x equal the sum of numbers of dots on the upper…

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Q: Example 39. The first twelve letters of the alphabet are written down at random. What is the…

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Q: 40% being retail accounts. These different accounts are processed by the retail and wholesale…

A: We have ,  P(Retail division) = 0.4 P(Wholesale division) = 1 - 0.40 = 0.6  P(Error | Retail…

Q: A bag of colored candies contains 200 pieces of candy in six different colors. There are 50 brown,…

A: Given data, Color No of candies Brown 50 Red 20 Yellow 40 Green 30 Orange 10 Blue 50…

Q: Rework problem 17 from the Chapter 2 review exercises in your text, involving the rolling of two…

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Q: In a two dice toss, what is the probability of event A (red die show 6) and event B (green die show…

A: When two dice are rolled the sample space is n(s)=62 = 36   Let A be the event that 1st die is 6 B…

Q: What is the probability of a standard dice roll being even or prime? 5/6 O 7/6 1/6 1/2

A: Given that  A standard dice is rolled  Sample space = S = ( 1 , 2 , 3 , 4 , 5 , 6 ) Even or prime =…

Q: 4. A university is offering two courses, one in Statistics and the other in Mathematics. These…

A: Number of students=300  Number of students in Statistics=85 Number of students im Mathematics=65…

Q: What is the probability of rolling two six-sided dice and obtaining the following numbers? a. 2 and…

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Q: In a game of Yahtzee, five balanced dice are rolledsimultaneously. Find the probabilities of…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: QI// 1- There are 6 different routes from Ibri to Sur and 5 different routes from Sur to Salalah.…

A: Question - 1: Given: There are 6 different routes from Ibri to Sur and 5 different routes from Sur…

Q: 3. (Rosner book – Page 110, Q: Infectious Disease) A study considered risk factors of HIV infection…

A: Given : Light users=40% Heavy users =55%   Note :As per guidelines only first 3 subparts have been…

Q: Example 8.4 An educational institution has offered admission to 100 students. On an average, the…

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Q: Poker Chips. A bowl contains 12 poker chips—3 red, 4 white, and 5 blue. If one of these poker chips…

A: a) The required probability is obtained as follows:

Q: 4-) You enter a chess tournament where your probability of winning a game is (0.3) against half the…

A: Let Bi be the event of playing With an opponent of type i so  P(B1)=0.5,P(B2)=0.25,P(B3)=0.25 Let W…

Q: spital lottery, 2.4 million tickets are sold; there are 16 grand prizes of new homes worth…

A: Total number of tickets sold = 2.4 million = 2,400,000   Number of tickets having second prize = 70.…

Q: Example 10.13 It has been found that 7 per cent of the tools manufactured by a factory are…

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Q: 3. You roll a pair of fair dice, one blue and the other gray. (a) (5 pts) What is the probability…

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Q: Consider a lotto game as described in Example 4. Assume that the balls numbered 8, 9 and 10 are…

A: Let the probability of getting any number from 1 to 7 is = x So the probability of getting 8 or 9 or…

Q: Two players A and B toss an unbiased die alternatively. He who first throws a six wins the game. If…

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Q: 14. A pair of dice is thrown. If it is known that one die shows a 4, what is the probability that a)…

A: A pair of dice is thrown. If it is known that one die shows a 4,

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.