Tutorials
Learn how to use each probability model effectively with best practices and examples
Getting Started
Relative Probability uses natural language processing to understand your probability questions. Simply type your question in plain English, and our system will identify the appropriate model and calculate the results.
Basic Query Structure
Most queries follow this pattern:
- Action: What you want to calculate (probability, chance, likelihood)
- Event: What you're analyzing (coin flip, dice roll, etc.)
- Parameters: Specific values or conditions
Example Query Structure:
"What is the probability of getting heads when flipping a coin 5 times?"
Action: "probability"
Event: "getting heads"
Parameters: "5 times"
Coin Flip Calculations
Coin flip models calculate probabilities for binary outcomes with equal probability (50/50).
When to Use
- Simple binary decisions or outcomes
- Educational probability examples
- Basic statistical understanding
Input Parameters
- Number of flips: How many times you flip the coin
- Desired outcome: Heads, tails, or specific sequences
Example Queries:
Flip a coin 10 times
What is the probability of getting 3 heads in 5 coin flips?
Probability of at least 2 heads when flipping 4 coins
Best Practices:
- Clearly specify the number of flips
- Use "heads" or "tails" for single outcomes
- For multiple outcomes, specify "at least," "exactly," or "at most"
- Start with simple queries before moving to complex sequences
Dice Roll Calculations
Dice models handle discrete uniform distributions where each outcome has equal probability.
When to Use
- Gaming probability calculations
- Discrete uniform distribution problems
- Multiple independent events
Input Parameters
- Number of dice: How many dice to roll
- Die type: 6-sided (default), 4-sided, 8-sided, etc.
- Target outcome: Specific numbers or sums
Example Queries:
Roll two dice
Probability of rolling a 7 with two 6-sided dice
What are the chances of getting at least one 6 when rolling three dice?
Roll a 20-sided die
Best Practices:
- Specify the number of sides if not standard 6-sided
- Use "sum" when referring to total of multiple dice
- Be clear about "at least," "exactly," or "at most" for ranges
- Consider independence when rolling multiple dice
Normal Distribution
Normal distributions model continuous data that clusters around a mean with symmetric spread.
When to Use
- Height, weight, test scores, measurement errors
- Financial returns, manufacturing tolerances
- Any naturally occurring continuous variable
Input Parameters
- Mean (μ): Center of the distribution
- Standard deviation (σ): Measure of spread
- Value or range: What you want to calculate probability for
Example Queries:
Normal distribution with mean 100 and standard deviation 15
Probability of scoring above 120 on a test with mean 100 and std dev 15
What percentage falls between 85 and 115 in a normal distribution with mean 100, std 15?
Best Practices:
- Always specify both mean and standard deviation
- Use realistic values for your context
- Remember that 68% of data falls within 1 standard deviation
- Consider if your data truly follows a normal pattern
Common Mistakes:
- Using normal distribution for discrete data
- Forgetting to specify standard deviation
- Using negative standard deviation
- Applying to data that isn't bell-shaped
Binomial Distribution
Binomial distributions model the number of successes in a fixed number of independent trials.
When to Use
- Quality control testing
- Medical treatment success rates
- Survey responses (yes/no questions)
- Marketing conversion rates
Input Parameters
- Number of trials (n): How many attempts
- Probability of success (p): Success rate per trial
- Number of successes (k): How many successes you want
Example Queries:
Binomial distribution with 20 trials and 30% success rate
Probability of exactly 5 successes in 15 trials with 40% success rate
At least 8 successes in 12 trials with probability 0.6
Best Practices:
- Ensure trials are independent
- Verify constant success probability
- Use percentages or decimals for probability
- Consider normal approximation for large n
Poisson Distribution
Poisson distributions model the number of events occurring in a fixed interval of time or space.
When to Use
- Website visits per hour
- Phone calls to a call center
- Defects in manufacturing
- Radioactive decay events
Input Parameters
- Rate (λ): Average number of events per interval
- Number of events (k): Specific count you want probability for
Example Queries:
Poisson distribution with rate 5
Probability of exactly 3 events with average rate of 4.5
No more than 2 calls in an hour with average of 6 calls per hour
Best Practices:
- Events should be rare and independent
- Rate should remain constant over the interval
- Use for counting events, not measurements
- Ensure events cannot occur simultaneously
Monte Carlo Simulation
Monte Carlo methods use random sampling to solve complex probability problems that are difficult to calculate analytically.
When to Use
- Complex systems with multiple variables
- Financial risk modeling
- Project timeline estimation
- When analytical solutions are impractical
Input Parameters
- Number of simulations: How many trials to run
- Variable distributions: Define each random variable
- Target outcome: What you want to measure
Example Queries:
Monte Carlo simulation with 10000 trials
Simulate portfolio returns with normal distribution
Project completion time simulation with uncertain tasks
Best Practices:
- Use more simulations for more accurate results
- Clearly define all random variables
- Validate results with known analytical solutions when possible
- Consider computational time vs. accuracy trade-offs
Bayesian Analysis
Bayesian methods update probabilities as new evidence becomes available.
When to Use
- Medical diagnosis with test results
- Spam filtering
- A/B testing analysis
- Updating beliefs with new data
Input Parameters
- Prior probability: Initial belief
- Likelihood: Probability of evidence given hypothesis
- Evidence: New information observed
Example Queries:
Bayesian update with prior 0.3 and likelihood 0.8
Medical test with 95% accuracy and 1% disease prevalence
Update probability after positive test result
Best Practices:
- Use informed priors when available
- Consider the quality of your evidence
- Update incrementally as new data arrives
- Validate with subject matter experts
Exponential Distribution
Exponential distributions model the time between events in a Poisson process.
When to Use
- Time until next customer arrival
- Component lifetime analysis
- Time between phone calls
- Radioactive decay timing
Input Parameters
- Rate parameter (λ): Events per unit time
- Time value: Specific time you want probability for
Example Queries:
Exponential distribution with rate 0.5
Time until next customer with average wait of 10 minutes
Probability of waiting more than 15 minutes
Best Practices:
- Verify the memoryless property applies
- Use for continuous time intervals
- Ensure constant rate over time
- Consider if events are truly random
Hypothesis Testing
Statistical tests to determine if observed data supports or contradicts a hypothesis.
When to Use
- A/B testing for website changes
- Quality control testing
- Research study validation
- Comparing groups or treatments
Input Parameters
- Null hypothesis: What you're testing against
- Alternative hypothesis: What you suspect is true
- Significance level: Usually 0.05
- Sample data: Your observations
Example Queries:
T-test with sample mean 105, population mean 100, alpha 0.05
Test if conversion rate changed from 5% baseline
Two-sample test comparing group A and group B
Best Practices:
- Define hypotheses before collecting data
- Use appropriate test for your data type
- Check assumptions (normality, independence)
- Consider practical significance, not just statistical
Stock Price Simulation
Models stock price movements using geometric Brownian motion for financial analysis.
When to Use
- Option pricing models
- Portfolio risk assessment
- Investment strategy backtesting
- Financial planning scenarios
Input Parameters
- Initial price: Starting stock price
- Expected return (μ): Annual drift rate
- Volatility (σ): Annual standard deviation
- Time period: Duration to simulate
Example Queries:
Stock simulation starting at $100, 8% return, 20% volatility
Simulate Apple stock for 1 year with historical parameters
Portfolio simulation with multiple assets
Best Practices:
- Use historical data to estimate parameters
- Run multiple simulations for robust results
- Consider transaction costs and dividends
- Validate against historical performance
Common Mistakes:
- Using unrealistic volatility values
- Ignoring market conditions and trends
- Over-relying on historical patterns
- Not accounting for extreme events
General Tips for Success
Query Writing Tips
- Be specific with your parameters
- Use clear, natural language
- Start simple and add complexity gradually
- Include units when relevant (minutes, dollars, etc.)
Interpreting Results
- Always read the explanation provided
- Check if results make intuitive sense
- Consider the assumptions of your chosen model
- Use visualizations to understand distributions
Model Selection
- Match the model to your data type (discrete vs. continuous)
- Consider the underlying assumptions
- Start with simpler models before moving to complex ones
- Validate results with domain expertise
Pro Tips:
- Save frequently used queries for quick access
- Export results for documentation and sharing
- Use the calculation history to track your analysis
- Experiment with different parameters to understand sensitivity