Simulation
Definition
Simulation is the process of imitating or replicating a real-life situation or event using a mathematical model. It allows us to study and analyze outcomes that would be difficult or impossible to observe directly.
Analogy
Imagine you want to know how likely it is for your favorite basketball team to win the championship. Instead of waiting for the actual games to happen, you create a computer program that simulates the tournament thousands of times. By running these simulations, you can estimate the probability of your team winning without actually playing any games.
Related terms
Trials: In simulation, trials refer to the number of times we repeat an experiment or scenario. Each trial represents one iteration of the simulation and helps us gather data on different outcomes.
Probabilities: Simulation often involves calculating probabilities, which represent the likelihood of certain events occurring. These probabilities are based on observed frequencies from multiple trials and help us make predictions about real-world scenarios.
Randomness: Simulations rely on randomness to mimic real-life uncertainty. By introducing random elements into our models, we can simulate unpredictable events and account for variability in outcomes.
"Simulation" appears in:
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Practice Questions (8)
Which of the following is an example of estimating a probability distribution with a simulation?
A statistics professor conducts a simulation to explore the probabilities of rolling different numbers on a six-sided die. The professor sets up the simulation to roll the die 10,000 times and records the outcomes. Which of the following statements is most likely to be true based on the simulation?
A student wants to conduct a simulation to estimate the probability of rolling a sum of 8 with two six-sided dice. Which of the following is the most appropriate method for conducting the simulation?
A simulation is conducted to estimate the probability of drawing a red card from a well-shuffled deck of playing cards. The simulation is repeated 1,000 times, and a red card is drawn 700 times. What can be concluded about the estimated probability based on this simulation?
A simulation is conducted to estimate the probability of rolling a number greater than 4 on a six-sided die. The die is rolled 500 times in the simulation, and a number greater than 4 is rolled 350 times. What is the estimated probability based on this simulation?
A simulation is conducted to estimate the probability of rolling a number less than or equal to 2 on a fair six-sided die. The die is rolled 200 times in the simulation, and a number less than or equal to 2 is rolled 50 times. What is the estimated probability based on this simulation?
Which of the following best describes the purpose of conducting multiple trials in a simulation?
A student conducts a simulation to estimate the probability of getting heads when flipping a fair coin. The coin is flipped 500 times in the simulation, and heads is observed 240 times. What is the estimated probability based on this simulation?
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