What is probability and how is it calculated?

Probability measures the likelihood of an event occurring. Basic probability = favorable outcomes ÷ total outcomes. For example, rolling a 3 on a 6-sided die: P = 1/6 ≈ 16.67%. Probability always falls between 0 (impossible) and 1 (certain).

What is conditional probability?

Conditional probability P(A|B) is the probability of event A occurring given that B has already occurred. Formula: P(A|B) = P(A and B) / P(B). Example: P(Queen | Face card) = (4/52) / (12/52) = 4/12 = 1/3.

What is the difference between 'and' and 'or' probability?

For independent events: P(A AND B) = P(A) × P(B) — both events must occur. For any events: P(A OR B) = P(A) + P(B) - P(A AND B) — at least one event occurs. For mutually exclusive events (can't both happen): P(A OR B) = P(A) + P(B).

What is binomial probability?

Binomial probability calculates the chance of getting exactly k successes in n independent trials, each with probability p. Formula: P(X=k) = C(n,k) × pᵏ × (1-p)^(n-k). Example: P(3 heads in 5 coin flips) = C(5,3) × 0.5³ × 0.5² = 10 × 0.125 × 0.25 = 31.25%.

What is the complement rule in probability?

The complement of event A (written A' or Ā) is the probability that A does NOT occur. P(A') = 1 - P(A). This is often easier to compute. Example: P(at least one head in 3 flips) = 1 - P(no heads) = 1 - (0.5)³ = 1 - 0.125 = 0.875.

How do you calculate dice probability?

For one die: P(specific number) = 1/6 ≈ 16.67%. For a sum with two dice: count favorable combinations out of 36 total. Example: P(sum=7) = 6/36 = 1/6 ≈ 16.67% (combinations: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1).

How do you calculate card probability?

A standard deck has 52 cards: 4 suits × 13 values. Examples: P(Ace) = 4/52 = 1/13 ≈ 7.69%, P(Heart) = 13/52 = 1/4 = 25%, P(Face card) = 12/52 = 3/13 ≈ 23.08%, P(Red card) = 26/52 = 1/2 = 50%.

What is the difference between probability with and without replacement?

With replacement: the item is returned before the next draw, so probability stays the same each time. Without replacement: the item is not returned, so the total decreases. Example: Drawing 2 aces from 52 cards. With replacement: (4/52)² = 0.59%. Without replacement: 4/52 × 3/51 = 0.45%.

Probability Calculator

Our Probability Calculator covers every type of probability problem you'll encounter in statistics, math class, or everyday life. Calculate basic probability from favorable outcomes, find conditional probability with P(A|B) formula, compute binomial probability for repeated trials, determine dice roll odds, and work out card draw probabilities. Every calculation comes with a clear step-by-step explanation so you can learn the method, not just get the answer.

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calendar_today Updated: April 2026

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Calculation Type

Favorable Outcomes

Total Outcomes

percent Result

P(A) =

16.67%

= 0.16667

1/6

Fraction

83.33%

P(Not A)

1 in 6

Odds

Formula

P(A) = k / n

format_list_numbered Step-by-Step Solution

Input Values

Calculation Type

functions Basic Probability

join Multiple Events

account_tree Conditional

bar_chart Binomial

casino Dice Roll

style Card Draw

Favorable Outcomes

Total Outcomes

auto_awesome AI Analysis

Enter your values and calculate to receive AI-powered insights about your results.

percent Key Probability Rules

Basic k / n

A AND B (indep.) P(A) × P(B)

A OR B P(A)+P(B)−P(A∩B)

Conditional P(A|B) P(A∩B)/P(B)

Complement P(A') 1 − P(A)

Binomial P(X=k) C(n,k)·pᵏ·qⁿ⁻ᵏ

casino Common Probabilities

Fair coin (heads) 50%

Die: specific number 16.67%

Card: specific value 7.69%

Card: specific suit 25%

Card: face card 23.08%

Two dice: sum = 7 16.67%

lightbulb Quick Tips

•P always between 0 and 1 (0% to 100%)
•Use complement when P(not A) is easier
•Multiply for AND (both must occur)
•Use addition rule for OR (either/both)
•Binomial: n trials, each with same p

How to Use This Calculator

Select Calculation Type

Choose from Basic, Multiple Events, Conditional, Binomial, Dice, or Card probability

Enter Your Values

Fill in the required numbers for your chosen calculation type

View the Result

See the probability as a fraction, decimal, and percentage

Read the Steps

Follow the step-by-step explanation to understand the method

The Formula

Basic probability is the ratio of favorable outcomes to total outcomes. For multiple independent events: P(A and B) = P(A) × P(B). For any two events: P(A or B) = P(A) + P(B) - P(A and B). Conditional: P(A|B) = P(A and B) / P(B). Complement: P(A') = 1 - P(A).

P(A) = Favorable Outcomes / Total Outcomes

lightbulb Variables Explained

P(A) Probability of event A (0 to 1)
n Total number of possible outcomes
k Number of favorable outcomes
P(A|B) Conditional probability of A given B has occurred

tips_and_updates Pro Tips

Probability is always between 0 (impossible) and 1 (certain) — or 0% to 100%

For independent events: P(A AND B) = P(A) × P(B)

For mutually exclusive events: P(A OR B) = P(A) + P(B)

For any two events: P(A OR B) = P(A) + P(B) − P(A AND B)

Complement rule: P(NOT A) = 1 − P(A) — always easier to find what you don't want

Binomial probability: use when you have n independent trials each with probability p

Probability quantifies how likely an event is to occur. It ranges from 0 (impossible) to 1 (certain). In everyday terms, a 0.5 probability means a 50-50 chance. Our calculator handles all standard probability types used in statistics, math, gambling analysis, and science.

Basic probability divides favorable outcomes by total outcomes. For multiple independent events, multiply probabilities (AND) or use the union formula (OR). Conditional probability asks 'what if we already know B happened?' Binomial probability handles repeated independent trials like flipping a coin n times.

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