Math & StatisticsVerified: 2026-10-05
Probability Calculator
Calculate single event probability, complementary odds, two-event independent and mutually exclusive intersections, and binomial distribution probabilities.
Direct Answer:The probability of an event P(A) is the number of favorable outcomes divided by total possible outcomes: P(A) = n(A) / n(S). For example, rolling a 6 on a 6-sided die is 1 ÷ 6 = 16.67% (0.1667), with odds of 1 to 5.
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Adjust Parameters
Number of desired or winning outcomes
Total size of sample space
Probability of Event P(A)
16.67% (1 / 6)
Decimal: 0.166667 | Odds: 1 : 5
Simplified Fraction
1 / 6
Odds in Favor
1 : 5
Odds Against
5 : 1
Probability of Event NOT Occurring
83.33% (0.833333)
Step-by-Step Probability Derivation
- Favorable outcomes n(A) = 1
- Total sample space outcomes n(S) = 6
- Probability P(A) = n(A) ÷ n(S) = 1 ÷ 6 = 1 / 6 = 0.166667
- Percentage = 16.67%
- Complementary probability P(not A) = 1 − 0.166667 = 0.833333
- Odds in favor = 1 : 5 | Odds against = 5 : 1
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How Probability Calculator is Calculated
Transparent mathematical formulas and assumptions used across our financial engines.
Mathematical Formula
P(A) = \frac{n(A)}{n(S)} \quad | \quad P(A \cup B) = P(A) + P(B) - P(A \cap B) \quad | \quad P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
Variables & Legend
P(A)
Probability of Event A
n(A)
Favorable Outcomes
n(S)
Total Outcomes
n
Trials
p
Success Rate
Step-by-Step Calculation
- Count Outcomes:
n(A) \le n(S)Identify favorable cases and total cases.
- Divide:
P(A) = n(A) / n(S)Divide favorable by total to find decimal probability.
- Complement:
P(A') = 1 - P(A)Subtract from 1 to find failure probability.
Conventions & Assumptions
- Probability is always bounded between 0 (impossible event) and 1 (certain event).
- Odds in favor express the ratio of successes to failures (a : b), whereas probability expresses successes to total outcomes (a / (a + b)).
Frequently Asked Questions
Divide the number of favorable outcomes by the total number of possible outcomes. For example, drawing an Ace from a standard 52-card deck has 4 favorable outcomes out of 52 total cards: 4 ÷ 52 = 1/13 ≈ 7.69%.