Practice Statistical Simulation in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Using random number generation to model real-world processes and estimate probabilities or outcomes that are difficult to calculate theoretically.

Can't calculate the probability mathematically? Simulate it! Run the scenario thousands of times with random numbers and see what fraction of outcomes match your event. It's like conducting experiments without real resources.

Example 1

easy
You want to estimate the probability of getting exactly 2 heads when flipping 3 coins. Describe how to use a simulation with a random number generator to estimate this probability.

Example 2

medium
A cereal brand puts one of 6 different toy figurines in each box (equally likely). Use simulation to estimate how many boxes you need to buy to collect all 6 figurines.

Example 3

medium
A multiple-choice test has 10 questions, each with 4 options (one correct). A student guesses randomly on every question. Design a simulation to estimate the probability of passing (getting 6 or more correct).

Example 4

hard
Two players play a game where each rolls a die. If the sum is 7, Player A wins; otherwise Player B wins. Run a conceptual simulation of 20 trials with these random rolls: (4,3), (2,5), (6,1), (3,3), (5,2), (1,4), (6,6), (2,3), (4,4), (5,1), (3,4), (6,2), (1,1), (2,6), (5,5), (4,1), (3,6), (2,2), (6,3), (1,5). Estimate each player's probability of winning.
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