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

P(A)0.0000%
P(not A)100.0000%
Odds of ANever
P(B)0.0000%
P(not B)100.0000%
Odds of BNever

Combined Event Probabilities

Assuming events A and B are independent

0.0000%
P(A and B)
Both events occur
0.0000%
P(A or B)
At least one occurs
0.0000%
P(A ⊕ B)
Exactly one occurs
100.0000%
P(not A and not B)
Neither occurs
0.0000%
P(A and not B)
Only A occurs
0.0000%
P(B and not A)
Only B occurs

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

1

Basic Probability

P(A) = favorable outcomes / total outcomes

2

Complement Rule

P(not A) = 1 - P(A)

3

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