Probability Calculator

Calculate probability of events occurring. Essential for statistics, gambling, games, and decision-making.

How to Use Probability Calculator

1. 1.**Enter favorable outcomes** (number of successful outcomes)
2. 2.**Enter total outcomes** (total possible outcomes)
3. 3.**Click "Calculate Probability"** to get results
4. 4.**View probability** as decimal, percentage, odds, and fraction

Features

• •**Multiple Formats**: Decimal, percentage, odds, fraction
• •**Real-time Calculation**: Instant probability results
• •**Odds Calculation**: Both for and against
• •**Fraction Display**: Simplified probability representation

Probability Formula

P(A) = Number of Favorable Outcomes / Total Number of Outcomes

Probability Types

• •**Theoretical Probability**: Based on mathematical analysis
• •**Experimental Probability**: Based on actual trials
• •**Subjective Probability**: Based on personal judgment
• •**Conditional Probability**: P(A|B) = P(A ∩ B) / P(B)

Common Applications

• •**Games**: Dice rolls, card games, board games
• •**Statistics**: Research, data analysis, predictions
• •**Finance**: Risk assessment, investment decisions
• •**Quality Control**: Defect rates, success rates
• •**Everyday**: Weather forecasts, sports predictions

Probability Examples

• •**Coin Flip**: 1 favorable, 2 total = 0.5 or 50%
• •**Die Roll**: 3 favorable (1,2,3), 6 total = 0.5 or 50%
• •**Card Draw**: 13 hearts, 52 cards = 0.25 or 25%
• •**Lottery**: 1 winning, 1,000,000 total = 0.000001 or 0.0001%

Odds vs Probability

• •**Probability**: P = favorable/total (0 to 1)
• •**Odds For**: favorable:unfavorable
• •**Odds Against**: unfavorable:favorable
• •**Conversion**: Odds = P/(1-P)

Probability Rules

• •**Addition Rule**: P(A or B) = P(A) + P(B) - P(A and B)
• •**Multiplication Rule**: P(A and B) = P(A) × P(B|A)
• •**Complement**: P(not A) = 1 - P(A)
• •**Range**: 0 ≤ P ≤ 1 (always between 0 and 1)

Tips for Using Probability Calculator

• •**Count outcomes carefully** for accurate results
• •**Consider all possibilities** in total outcomes
• •**Check for independence** when combining events
• •**Use appropriate format** for your application
• •**Remember limitations** of probability theory

Common Misconceptions

• •**Gambler's Fallacy**: Past events don't affect future
• •**Hot Hand Fallacy**: Streaks don't change probability
• •**Law of Large Numbers**: Results approach probability over many trials
• •**Independence**: Some events are related, not independent