1) How many outcomes are possible from tossing a coin and rolling a 6-sided die?

Q: How many rolls would it take for 1,000 dice to be reduced to 500 dice? (Assume all the dice are…

A: Assume that all dice are 6-sided and unbiased.The objective is to find the number of rolls it would…

Q: probability

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Q: what is the possible outcomes in tossing a coin 3 times?

A: Given :  Tossing a coin 3 times

Q: You roll an 8-sided die.  (It has the numbers 1 - 8)  Is rolling a number greater than 4 a simple or…

A: Simple event: when there is only one outcome in an experiment. For example: Tossing a coin getting…

Q: Two six-sided dice are rolled and their product is taken. How many elements are in the subset of…

A: When two six-sided dice are rolled the sample space is as shown below  (1,1), (1,2),(1,3),…

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: An unusual die has the numbers 4​, 4​, 5​, 5​, 7​, and 7 on its six faces. Two of these dice are​…

A: Given that the unusual die has faces 4, 4, 5, 5, 7 and 7. Two of the dice are rolled. The total…

Q: A​ single, fair​ 6-sided die is tossed. Find the odds in favor of rolling a 2, 3, or 6

A: It is given that the die is faired and has 6 sides. Therefore all the 6 faces are equally likely to…

Q: An unusual die has the numbers 5​, 5​, 6​, 6​, 8​, and 8 on its six faces. Two of these dice are​…

A: Different numbers of dice are {5,6,8}.  For any of the 3 different on the first die, 3 different…

Q: There are   possible outcomes when you flip four fair coins.

A: Ans- There are  possible outcomes when you flip four fair coins.

Q: When playing the dice game 21's, if you were presented with the following scenario, how many dice…

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Q: what is the probablity of rolling one six-sided die and obtaining a 5 or a 6

A: To calculate the probability that either 5 or 6 turns up when a 6 sided die is rolled

Q: Compute the probability of rolling a 12-sided die and getting a number other than 8.

A: Probability: The formula for probability of an event E is as follows:

Q: A game of chance involves rolling a standard, six-sided die. The amount of money the player wins…

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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: Allottery exists where balls numbered 1 to 20 are placed in an urn to win. You must match the four…

A: Given information:A lottery involves balls numbered from 1 to 20 placed in an urn.Total number of…

Q: 2. Determine whether the second scenario would be dependent or independent of the first scenario.…

A: Independent events are those in which outcome of one event doesn't affect the probability of the…

Q: Compute the probability of tossing a six-sided die and getting an even number.

A: When we toss a six-sided die then the possible outcomes are S = { 1,2,3,4,5,6}  = n(S) = 6 Formula…

Q: When tossing a fair coin six times, what is the chance of getting three heads. (give full answer…

A: Given Information: Number of trials (n) = 6 Number of successes (r) = 3  Probability of success i.e.…

Q: to get the 7 macrostate?

A: here rolling two dice at at a time and add thier outcomes to get macrostate

Q: Determine the probability p of an even number appearing in the toss of a fair die.

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Q: 3. Consider the experiment where you roll a special 4-sided die once and then pick one of two colors…

A: There is a four sided die which is rolled once and then a ball is picked from the jar which is…

Q: Consider rolling one regular, six-sided die until you get the first one. You may leave answers in…

A: Geometric distribution In series of Bernoulli trials, the random variable X denotes number of trials…

Q: 2) Choose the correct answer. Sherane rolls a standard, six-sided number cube. What is the…

A: We know that total faces on die is 6  So N= 6  And there are two multiple of 3 on the die i.e. 3 and…

Q: The number of possible outcomes of the rolling of a die and then tossing a coin is 8. True False

A: We have to solve given problem:

Q: What is the probability of rolling a fair six-sided die and getting an odd number?

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Q: 5. Danielle flips her coin three times. What are her chances of getting three straight heads or…

A: We know that  Sample space=S S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

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: you toss a pair of dice. a) determine the number of possible pairs of outcomes.

A: Die is a traditional cube it has a 6 faces.Total number of outcomes for two dice are,

Q: How many different outcomes are possible for 6 rolls of a die?

A: From the provided information, A die is rolled 6 times.

Q: First a coin is tossed and then a four-sided die is rolled. How many possible outcomes are there? O…

A: Sample space of a coin is  toss and a four sided die is rolled.  {H,T} and {1,2,3,4}

Q: 2. John plans to toss a die until he observes two even numbers. What is the chance tha the 2nd even…

A: The sample space of a dice is S= {1, 2, 3, 4, 5, 6}. The probability of getting odd number is 1/2.…

Q: 8 dice are tossed. How many times do you expect at most 3 dice to show a number less than 3?

A: Given: n = 8  possible outcomes of a die: 1 , 2 , 3 , 4 , 5 , 6 Total number of outcomes = 6 Number…

Q: Develop a hypothesis statement. Predict how often a two-die total of six will occur if each person…

A: The objective of this question is to develop a hypothesis statement predicting the frequency of a…

Q: Select all possible outcomes for spinning the spinner and flipping a fair coin

A: The objective of the question is to identify all possible outcomes when two independent events occur…

Q: 7. Rolling Dice If five dice are rolled, how many different outcomes are there?

A: Multiplication rule for counting:Consider the total number of events in an experiment is n.The…

Q: Suppose we roll a fair 6-sided dice once. a) Find the probability of rolling a 3 b) Find the…

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