Probability Math Question (Simulation)?
OK, so the Question is: Describe a Simulation you could use to estimate the probability of guessing answers and scoring 70% on a multiple choice question test that has 10 questions and each question has 5 answers. This is a Simulation Question in probability and I could really use some help could you please tell me how you would do this question and explain it. Thanks!
How do you solve these probability simulation problems using the following information?
Main Street Supermarket randomly gives each shopper a free two-liter bottle of cola during the Saturday shopping hours. The supermarket sells 6 different types of cola. 1. What could be used to perform a simulation of this situation? 2. How could you use this simulation to model the next 50 bottles of cola given out? 3. At a picnic, there were 2 peanut butter sandwiches, 2 chicken sandwiches, a tuna sandwich, and a turkey sandwich in a cooler. Describe a simulation that could be used to find the probability of randomly picking a certain sandwich from the cooler.
What is the probability that the universe is a computer simulation?
Elon Musk’s argument: “the probability that this universe is base reality and not a computer simulation is one in a billion” is a sound and logical argument. (If you’re not aware of his full argument, google the video)However, the argument seems to lack an understanding of meta-probability. Understanding meta-probabilities allows us to better contextualize/interpret the argument.A quick example:1. What is the probability that a fair coin toss results in heads? 50%2. If you are told a red team is playing a blue team at soccer this afternoon, and you are asked to predict the result - what is the probability that the blue team will win? 50%3. If you are now told that the “blue team” is the French national soccer team, and the “red team” is made up of local school children, what is the probability that the blue team will win?…. Now that we have more information, it’s no longer 50%… it’s now more like 99.999%What’s going on here? Whilst in examples 1. and 2. both probabilities are 50% at face-value, they are actually quite different. The problem stems from the fact that when stating a probability, the uncertainty of the probability is rarely stated. The reality, when comparing the probabilities of a fair coin toss with a random soccer game (1. and 2.) looks like this:As you can see above, whilst both probabilities are stated as 50%, the meta-probabilities are shown by the curves. The curves reveal that the coin toss result is known to be a 50% chance fairly accurately, but the soccer game result is known to be 50% with a large amount of uncertainty.In example 3. we acquire more information about the teams playing, and this allows us to make a better prediction of the result. In other words: The less information we have about the system/process we are trying to predict, the greater the uncertainty in our probabilities.So whilst I agree that: “with the information we have at present, it seems logical that there is a one in a billion chance that we are not in a simulation”, the information we have about the universe is but a speck of the total information available about the universe (the entire system/process). We mainly know a lot about ourselves and Earth in this time-period. This is highly likely to skew predictions and give them bias.I’m not pretending to know whether we live in base reality or in a simulation. But I can say that the uncertainty in Elon’s probability is so great that it is no longer a meaningful/reasonable prediction.
How am I suppose to describe a simulation procedure?
I am assuming that the population of adult consumers is so large that the effect of selecting without replacement (instead of with replacement) is insignificant. A good scientific calculator or computer generally can select random decimals from a uniform distribution in the interval (0, 1). Note that a given randomly selected decimal has probability 0.95 of being less than 0.95 . Select 50 of these decimals on the computer or calculator. For each decimal, we can say that the consumer recognizes McDonald's if the decimal is less than 0.95, and does not recognize the name if the decimal is 0.95 or greater. Lord bless you today!
Probability and Binomial Distributions?
1)Suppose you buy four boxes of the Kraked Korn Cereal. Remember that each box has an equal probability of containing any one of the seven collector cards a)what is the probability of getting 1)four identical cards 2)three identical cards 3)two identical and two different cards 4)two pairs of identical cards 5)four different cards 2)The local newspaper publishes a trivia contest with 12 extremely difficult questions, each having 4 possible answers. You have no idea what the correct answers are,so you make a guess for each question a)explain why this situation can be modelled by a binomial distribution b)use a simulation to predict the expected number ofcorrect answers c)verify your prediction mathematically d)what is the probability that you will get atleast 6 answers correct e)what is the probability that you will get fewer than 2 answers correct f)describe how the graph of this distribution would change if the number of possible answers for each question incr. or decr
When running Monte Carlo simulations in situations where you're only interested in tail outcomes, is there a way to only simulate these outcomes so that you can come up with more reliable answers in fewer simulations?
Yes. This is known as “importance sampling”. There are a number of techniques for it. Usually, by the way, you’re most interested in outcomes on the border, such as the simulations between percentiles 0.9% and 1.1%, rather than the simulations between percentiles 0% and 1%.One simple approach is to bias all your random inputs. For example, suppose you have N random inputs, all uniform from zero to one, and defined in such a way that low numbers lead to bad outcomes (it won’t always be possible to do this, some bad outcomes could result from complex interactions of inputs, in which case, you don’t bias those inputs). Instead of using a uniform 0, 1 pseudo-random input, you square each input.Now each simulation run has a probability attached to it, they’re not all equally likely. Your going to have to weight each run by the product of all your biased variables. For example, if one simulation has inputs 0.1, 0.2, 0.1 and another has 0.8, 0.5, 0.9, the first one will get weight 0.002, and the second one weight 0.360, 180 times as much.The result is that your good outcomes are represented by a few point that have a lot of weight, while your bad outcomes are represented by many points with small weight. This gives you much more precision in your estimates of tail scenarios.
Experimental probability of compound events question. Need help, thanks!?
At a car wash, customers can choose the type of wash and whether to use interior vacuum. Customers are equally likely to choose each type of wash and whether to use the vacuum. Use a simulation to find experimental probability that the next customer purchases a deluxe wash and no interior vacuum. Describe your simulation.
Define a simulation by telling how you represent correct answers, incorrect answers, and the quiz.?
1. In this question, the events are independent. What you choice for question 1 is, doesn't directly affect what your answer for questions 2 is. So you can use the multiplication rule. The multiplication rule states that if the chance that one event will happen is not influenced by whether or not a second event happends, the probability that both events will occur is the product of their seprate probabilities. so you have 4 questions with the probability of guessing the correct answer of 50%, and the incorrect answer is 50%. you are asked what the probability is that you get three correct out of four. Since order doesn't matter you just multiply .5x.5x.5=.125 OR 12.5% 2. The same goes for this questions, except the probability of gett a correct answer is .25. so you need to do .25*.25*.25*.25= .003906 OR .3906%