Statistical Simulation Statistics Example 3

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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).

Solution

  1. 1
    Step 1: For each question, generate a random integer 1–4. If the result is 1, the guess is correct. Count the number of correct answers out of 10.
  2. 2
    Step 2: Repeat for many trials (e.g., 10,000). Count how many trials have 6 or more correct. Estimated P(pass)=trials with ≥6 correcttotal trialsP(\text{pass}) = \frac{\text{trials with } \geq 6 \text{ correct}}{\text{total trials}}. The true probability is very low (~2%).

Answer

Generate 10 random integers (1–4) per trial, count correct (=1), repeat many times. Estimate P(pass) as fraction with 6+ correct. Expected: approximately 2%.
Simulation allows us to estimate probabilities for multi-step random processes without complex combinatorial calculations. By running thousands of simulated tests, we can reliably estimate the probability of passing by random guessing.

About Statistical Simulation

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

Learn more about Statistical Simulation →

More Statistical Simulation Examples

Example 1 easy

You want to estimate the probability of getting exactly 2 heads when flipping 3 coins. Describe how

Example 2 medium

A cereal brand puts one of 6 different toy figurines in each box (equally likely). Use simulation to

Example 4 hard

Two players play a game where each rolls a die. If the sum is 7, Player A wins; otherwise Player B w

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