If two fair dice are rolled together, which of the following is more likely:  i)Getting a total of 7 or more. ii) Getting a total of 7 or less.

Q: In the tossing of two dice simulatneously; the probability of getting a total of 7 on the upper…

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Q: When two balanced dice are rolled,there are 36 possible outcomes.What is the probability that the…

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Q: If two fair dice are thrown, what are the odds of obtaining a sum of 10?

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Q: If six face dice is rolled once, what is the probability of getting less than 3 on it

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Q: If two balanced dice are rolled, what is the probability that the sum of  two numbers that appear…

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Q: i) Find the probability that, when 5 fair six-sided dice are rolled, the result is: a) 5-of-a-kind…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: If n fair six-sided dice are tossed and the numbers show- ing on top are recorded, how many

A: (a) Suppose that the tasks T1, T2,..., Tk are to be performed in sequence. If T1 can be performed in…

Q: The set of all outcomes of rolling two distinguishable dice such that the numbers add to 9.

A: Each dice have six outcomes. We use this basic rule to solve the problem

Q: What is the probablity of rolling a 2 or a 4 on a dice?

A: a dice have 6 sides  all outcomes are equally possble s : {1,2,3,4,5,6}   p(roll 2 or 4) = ?

Q: 1. If two fair dice are rolled, what is the probability that the sum will be greater than or equal…

A: We first make a table for the outcomes when two dice are rolled. sum Outcomes Number of…

Q: If we roll three six-sixed dice, what's the probability that all three show even number

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Q: here are four dice rolled once, what is the probability of getting 22 or more?

A: From the given information we find the probability.

Q: What is the fewest number of times you must roll a six-sided dice before you can be assured that n…

A: The Pegion Hole Principle: Suppose that  and  are natural numbers and that we are distributing…

Q: In rolling two fair dice, what is the probability of obtaining equal numbers or numbers with an even…

A: Probability: Probability is a chance factor that occurs at every outcome of a random experiment.It…

Q: What is the probability that at least one of a pair of dice is smaller than 4, given that the sum of…

A: Given, the sum of the pair of dice is 8,9,10,11,12. Now for sum to be equal to 8, the outcomes will…

Q: How many dice must be thrown so that there is a better than even chance of obtaining at least one…

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Q: Suppose you roll two five-sided dice (each with sides labeled 1 through 5).  What is the probability…

A: The sample space for two five-sided dice is : S= {(1,1)(1,2)(1,3)(1,4)(1,5)…

Q: If two balanced dice are rolled, what is the probability that the difference between the two numbers…

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Q: What is the probability of rolling seven dice and getting at least one matched pair?

A: From the provided information, Seven dice are rolled. The total outcomes rolling 7 dice = 67 The…

Q: Three unbiased dice are rolled. What is the probability that they all show different faces?

A: It is given that three unbiased dice are rolled. It is known that every dice has 6 faces. The main…

Q: In rolling a pair of fair dice, what is the probablity of rolling a sum of ten?

A: The provided information is  The rolling a fair dice. The sample space is…

Q: Two ordinary six-sided dice are rolled. What is the probability of getting a sum of 8?

A: Since. it is given that two six-sided dice are rolled, Our Aim is to tellwhat is the probability of…

Q: On average, how many dice would you expect to show a "4"? die (dice)

A: Geometric distribution is the probability distribution of the number X of Bernoulli trials needed to…

Q: There are four dice rolled once, what is the probability of getting 22 or more

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Q: How many possible outcomes would there be if four dice were rolled?

A: we know that if n dice are rolled than the possibleoutcomes are6×6×6×6×.......×6ntimes=6n

Q: if you roll a pair of fair dice, what is the probability of getting a sum of 1

A: Roll a pair of fair dice, Sample space = S= (1,1) (1,2) (1,3) (1,4) (1,5)…

Q: In rolling 2 fair dice, what is the probability of a sum greater than 3 but not exceeding 6?

A: The two fair dices are rolled, the pairs whose sum is greater than 3 but not exceeding 6 are (1, 3),…

Q: How many dice must be thrown so that there is a better than even chance of obtaining a six?

A: A single dice contains 6 numbers { 1, 2 ,3 , 4 , 5 , 6} There is a equal chance of getting any…

Q: If we roll three six-sixed dice, what's the probability that their sum is even?

A: Further counting arguments can be used to find the number of ways of forming the other sums. The…

Q: 1. Obtain the probability of adding up six points if we toss three distinct dice.

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: 1. In rolling two dice, what is the probability of landing same numbers?

A: Since you have posted multiple questions, we are answering the first one. if any doubt, kindly…

Q: 2. If two fair dice are rolled, what is the probability of getting a sum greater than 11 or a sum…

A: If two fair dice are rolled, we need to find the probability of getting a sum greater than 11 or a…

Q: What is the probability of getting a total of 9 (a) twice and (b) at least twice in 6 tosses of a…

A: Here use binomial distribution  Each trial is independent  Finite number of trial (n=6) Probability…

Q: what is the probability of getting a total of 8, 9, or 11 when a pair fair of dice is tossed

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Q: What is the probability of getting either a three or a four on at least one the two dice?

A: From the provided information, Total outcomes = 36

Q: If two balanced dice are rolled, what is the probability that the difference between the two numbers…

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Q: What is the probability that at least one of a pair of fair dice lands of 5, given that the sum of…

A: Given At east one of a pair of fair dice lands of 5, The sum of the dice is 9

Q: The expected number of times a fair dice shows the number 6 in six independent rolls is equal to 1.…

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Q: In rolling 3 fair dice, what is the probability of obtaining a sum not greater than 16?

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Q: 4. If five Pentagonal trapezohedron dice (10-sides) are rolled, what is the probability that each of…

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Q: suppose you roll a pair of fair 6 sided dices what is the probability that one of the rolls is an…

A: If two 6 sided dice are rolled then sample space is given by-…

Q: Suppose you roll two five-sided dice (each with sides labeled 1 through 5). What is the probability…

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Q: 2. A pair of dice is rolled thrice. What is the probability of getting doubles in the three rolls?

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Q: A fair dice is rolled four times.  What is the probability of obtaining a 3,2,3 and 3 in that order?

A: For any event A and the sample space S, the probability can be found as,

Q: If two fair dice are rolled, find the probabilities of the following results.A sum of 8, given that…

A: Consider the following events, A=the sum of outcomes is greater than 7B=the sum of outcomes is equal…

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.