Probability Calculator
Calculate event probabilities and combinations
Find the probability of an event and its complement
P(A) = favorable outcomes / total outcomesWhat is a Probability Calculator?
A Probability Calculator is a math tool that helps you find the likelihood of an event happening without doing the calculations manually. Probability measures chance as a number between 0 and 1, where 0 means an event is impossible and 1 means it is certain. Probabilities are also commonly written as percentages (0% to 100%) or as fractions.
Probability is used in many real-world situations: predicting outcomes in games (coins, dice, cards), analyzing risk in finance and insurance, estimating outcomes in science and medicine, and making decisions under uncertainty. Even simple probability skills can help you interpret data and understand everyday "odds."
This calculator is useful for quickly computing probabilities for common scenarios—like "favorable outcomes vs total outcomes"—and, depending on the calculator features, it may also help with combined events (AND/OR), complements (NOT), or conditional probability.
How to Use This Probability Calculator
- Choose the probability type -- such as single-event probability, two events (AND / OR), or conditional probability
- Enter the required values -- such as favorable outcomes (successes), total outcomes (all possible outcomes), or probabilities for Event A and Event B
- Click "Calculate" -- to get the probability
- Review the result -- in decimal, fraction, or percent (depending on what the calculator displays)
- Double-check assumptions -- equally likely outcomes, independence, and whether events overlap
Tips:
- Make sure total outcomes is greater than zero
- If you're using counts (favorable/total), the outcomes should be based on the same sample space
- For multi-event probability, confirm whether events are independent (one does not affect the other) or dependent (one affects the other)
Probability Formulas
Basic Probability (Equally Likely Outcomes)
P(A) = Favorable outcomes / Total outcomes
The ratio of successful outcomes to all possible outcomes
Complement (NOT A)
P(not A) = 1 − P(A)
The probability of an event NOT happening
Conditional Probability
P(B|A) = P(A ∩ B) / P(A)
Probability of B given that A has occurred
Addition Rule (A OR B)
Mutually exclusive events
P(A ∪ B) = P(A) + P(B)
Cannot happen at the same time
Overlapping events
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Subtract the overlap to avoid double-counting
Multiplication Rule (A AND B)
Independent events
P(A ∩ B) = P(A) × P(B)
One does not affect the other
Dependent events
P(A ∩ B) = P(A) × P(B|A)
One event affects the other
Example Calculations
Example 1: Coin Flip (Heads)
Setup: A fair coin has 2 equally likely outcomes
Favorable outcomes: 1 (Heads)
Total outcomes: 2
Calculation: P(Heads) = 1/2 = 0.5 = 50%
Result: 50%
Example 2: Rolling a 4 on a Die
Setup: A standard die has 6 outcomes (1–6)
Favorable outcomes: 1 (rolling a 4)
Total outcomes: 6
Calculation: P(4) = 1/6 ≈ 0.1667 = 16.67%
Result: 16.67%
Example 3: Rolling an Even Number
Even numbers on a die: 2, 4, 6
Favorable outcomes: 3
Total outcomes: 6
Calculation: P(Even) = 3/6 = 1/2 = 50%
Result: 50%
Example 4: Two Independent Events (AND)
Problem: Rolling a 6 AND flipping Heads
P(6): 1/6, P(Heads): 1/2
Calculation: P(6 AND Heads) = 1/6 × 1/2 = 1/12 ≈ 0.0833
Result: 8.33%
Example 5: A OR B with Overlap
Setup: Pick a random number from 1 to 10
A: "number is even" (2,4,6,8,10) → P(A) = 5/10
B: "number > 6" (7,8,9,10) → P(B) = 4/10
Overlap: A ∩ B = (8,10) → P(A ∩ B) = 2/10
Calculation: P(A ∪ B) = 5/10 + 4/10 − 2/10 = 7/10 = 70%
Result: 70%
Frequently Asked Questions
What does probability mean in simple terms?
Probability is the chance that something happens. It ranges from 0 (impossible) to 1 (certain), and it's often shown as a percentage from 0% to 100%.
What are "favorable outcomes" and "total outcomes"?
Favorable outcomes are the results you want (successes). Total outcomes are all possible results. For a die, total outcomes are 6; favorable outcomes depend on your event.
What's the difference between independent and dependent events?
Independent events do not affect each other (coin flip + die roll). Dependent events do affect each other (drawing two cards without replacement changes the second probability).
When can I add probabilities, and when should I not?
You can add probabilities when calculating A OR B, but if events overlap, you must subtract the overlap:
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
If events are mutually exclusive, the overlap is zero.
Why might a probability calculator result look "wrong"?
Common reasons include using the wrong sample space, assuming outcomes are equally likely when they aren't, mixing dependent and independent event rules, or forgetting overlap in OR problems.
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