An experiment of drawing two different dice one time, if the random variable X represents the absolute value of the difference between the appearing numbers, then X takes the values

Q: You have some number of coins in your pocket, and you choose two at random. The random variable Z…

A: The random variable Z assigns the value of the coins in cents to each outcome  you draw out a…

Q: A pair of dice is rolled. Find the probabilities of the given events.(a) The sum is 6. (b) The sum…

A: If a pair of dice rolled then the total number of outcomes= (6*6)=36 (because each throw has 6…

Q: Three statistics professors and seven chemistry professors are available to be advisors to a student…

A: Given, Three statistics professors and seven chemistry professors are available to be advisors to a…

Q: A pair of dice is rolled. Find the probabilities of the given events. (Enter exact numbers as…

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Q: A pair of fair dice is tossed. Find the probability that the maximum of the two numbers is greater…

A: Probability of an event is the chance of occurrence of that event and this is equal to ratio of…

Q: 4) A person is taking a 12-question multiple-choice test for which each question has three answer…

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Q: A race consists of 7 women and 10 men. Find the following probabilities for the top three finishers:…

A: The number of men is 10 and the number of women is 7.

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: You have two four-sided dice. Compute the following probabilities: Rolling an 8 Rolling a 6

A: S={ (1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4) (3,1) (3,2) (3,3) (3,4) (4,1) (4,2) (4,3) (4,4)…

Q: Let the random variable Y = a + bX. Then, µy = bux. O True O False

A: Given statement isY=a+bX

Q: 13. What is the sum of the probabilities of all values of the random variable? C. ΣΡ(Χ)-1 D. ΣΡ(Χ)…

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Q: 1. If two coins are tossed, which is NOT a possible value of the random variable for the number of…

A: 1. Answer: Option D.

Q: You have the green and red dice. 1. What is the probability that the dice show the same numbers? 2.…

A: There are two dices green and red. The set showing number of events is, S=1, 1, 1, 2, 1, 3, 1, 4, 1,…

Q: A pair of dice is rolled. Find the probabilities of the given events. (Enter exact numbers as…

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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: 1. In a simultaneous throw of a pair of fair 6-sided dice, find the probability of getting: h. At…

A: Let 'S' be the sample space of rolling two fair dice together. S={1,1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6…

Q: You select a family with three children. If M represents a male child and F a female child, the…

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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: You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of…

A: Introduction: Two fair dice are rolled in the experiment. Each die has possible outcomes: {1, 2, 3,…

Q: A pair of dice is rolled. Find the probabilities of the given events.  (a) The sum is 12.

A: For a random experiment of throwing a pair of dice, the total number of possible cases is: ns=62=36…

Q: A pair of 6-sided dice are rolled. (a) What's the probability that neither die is a 2 if their sum…

A: If the probability of getting selected for each outcome is equal then such outcomes can be termed as…

Q: 5. A student rolls 2 fair 6-sided dice. What is the probability the sum of the numbers they roll is…

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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: You select a family with three children. If M represents a male child and F a female child, the…

A: Given that: M represent a male child. F represent the female child. Sample space = { MMM, MMF, MFM,…

Q: How many possible outcomes are there for getting a sum of 7 or 11 on a pair of dice? (Hint: Look at…

A: By throwing pair of dice , number of possible outcomes are :  Since we have only 2 dice.Check out…

Q: There is a 0.39 probability that John will purchase a new car, a 0.73 probability that Mary will…

A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

Q: A casino game works as follows: You have to pay $6 to play. Then you flip a fair coin and roll a…

A: There is total 12 possible outcomes i.e {(H,1), (H,2), .... (H,6), (T,1), (T,2)........(T,6)} Let X…

Q: 6. Which experiment has exactly 12 possible outcomes? (a) Flipping a coin six times (b) Rolling two…

A: A random experiment is an experiment that has multiple possible outcomes. These experiments can be…

Q: In rolling the dice two times , the probability that the sum of the two appearing numbers is greater…

A: We have to find correct answer....

Q: Suppose V, W,X, and Y are random variables. If V and W are

A: Always remember, When two variable is independent, then their correlation coefficient is zero…

Q: Casino games of pure chance (e.g. craps, roulette, baccarat, and keno) always yield a "house…

A: Hi! Thanks you for the question, As per the honor code, we are allowed to answer three sub-parts at…

Q: (5) If X is any random variable, then the inequality, \E[X]<E\X\ exists

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Q: A commuter passes through 3 traffic lights on her way to work and must stop at each one that is red.…

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Q: 1. A binomial experiment is one in which there are exactly outcomes. One outcome is called and the…

A: A binomial experiment is one in which there are exactly toe outcomes.

Q: If ​P(A)=4/5 compute the odds in favor of A resulting from a single trial of an experiment

A: Given, P(A) = 4/5 Implies, there are 4 in favor of A in total 5 trials of an experiment  No of…

Q: the number of girls (out of 2 children) in each family. Is this a random variable, and if it is,…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

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

A: Playing the half of the opponent pool, the probability of winning is 0.3 Playing the half of the…

Q: Example 35: Is it possible to determine the random variable X for which Pm - 3 ox <X<m+30x}= 0.3 ? |

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Q: If two fair dice are rolled together, which of the following is more likely:  i)Getting a total of…

A: i) The total outcome after rolling two fir dice together = 36 Possible outcomes getting a total 7 or…

Q: 4. The number of students entering in the canteen at any given hour is represented by a random…

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Q: 3. Nine percent of men and 0.25% of women cannot distinguish between the colors red and green. This…

A: P (men is color blind)=0.09n=6 mens selectedx=no. of men have color blindnessFollow binomial…

Q: The sum of the probabilities of all outcomes in the sample space 1. For any event A, –1 < P(A) < 1…

A: We have to check

Q: You toss a fair coin four times, and the random variable X assignsthe number of tails that appear in…

A: Consider the given information, The random variable X is the number of the tails appear in each…

Q: Consider the following experiment: Roll a pair of fair dice. Event A is getting an even sum. Event…

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Q: Part B In randomized response study participants are asked a sensitive question. For example, how…

A: Please check the solution below

Q: Consider the following game: A player rolls two dice. If he rolls 7 or less then he loses the game.…

A: While rolling a pair of dice, the possible outcomes are the natural numbers lying between 1 and 12.…

Q: ) A pair of fair dice is thrown 5 times. If getting a doublet (doubles) is considered to be success,…

A: S={ (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)  (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)  (3,1) (3,2) (3,3)…

Q: What do we mean when we say that two random variables are independent? (Briefly. You may use an…

A: Two random variables are independent if the product of marginal probability functions of them…

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: 1) If you roll a fair dice, what is the probability of rolling "2" or "3" given that the number of…

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Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.