Probability Calculator
Calculate probabilities for single events, combined events, and series of trials with comprehensive analysis
Probability Calculator
Enter as percentage (0-100)
Enter as percentage (0-100)
Number of independent trials or repetitions
Single Event Probabilities
Combined Event Probabilities
Assuming events A and B are independent
Formulas Used
Combined Events (Independent):
• P(A and B) = P(A) × P(B) = 0.0000 × 0.0000 = 0.0000
• P(A or B) = P(A) + P(B) - P(A and B) = 0.0000
• P(exactly one) = P(A)×P(not B) + P(B)×P(not A) = 0.0000
Example Calculation
Coin Flip and Die Roll
Event A: Getting heads on a coin flip (50%)
Event B: Rolling a 6 on a standard die (16.67%)
Question: What's the probability of getting both?
Solution
P(heads and 6) = P(heads) × P(6) = 0.5 × 0.1667 = 0.0833
Result: 8.33% chance of both occurring
Odds: 1 in 12 chance
Probability Concepts
Basic Probability
P(A) = favorable outcomes / total outcomes
Complement Rule
P(not A) = 1 - P(A)
Independence
P(A and B) = P(A) × P(B)
Probability Tips
Probabilities range from 0 (impossible) to 1 (certain)
Sum of all possible outcomes equals 1
Independent events don't affect each other
Use multiplication for "and", addition for "or" (with overlap correction)
Understanding Probability
What is Probability?
Probability is the measure of the likelihood that an event will occur. It's expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
Types of Probability
- •Theoretical: Based on mathematical reasoning
- •Experimental: Based on observed data
- •Subjective: Based on personal judgment
Key Formulas
Basic Probability
P(A) = Number of favorable outcomes / Total number of outcomes
Complement Rule
P(not A) = 1 - P(A)
Independent Events
P(A and B) = P(A) × P(B)
Addition Rule
P(A or B) = P(A) + P(B) - P(A and B)
Real-World Applications
Games of Chance
Dice, cards, lotteries, and casino games
Risk Assessment
Insurance, finance, and investment decisions
Medical Testing
Diagnostic accuracy and treatment outcomes