Statistics

Probability Calculator — Single & Combined Events

Find the probability of a single event from favorable and total outcomes, or combine two independent events with AND / OR logic — all shown as decimals, percentages, and odds.

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📝 Single Event Probability

🔄 Two Independent Events

📊 Single Event Result

Enter favorable and total outcomes

🔄 Combined Event Result

Enter P(A) and P(B) as percentages
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Disclaimer: This tool performs standard mathematical calculations for educational and reference purposes. Always double-check results independently for graded coursework, exams, or decisions involving real risk or money.

Understanding Probability

Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain). For a single event with equally likely outcomes, the probability is simply P(A) = favorable outcomes / total outcomes. That same value can be expressed three interchangeable ways: as a decimal (0.25), a percentage (25%), or odds (1 in 4) — pick whichever format fits how you're communicating the result.

Combining Two Independent Events

When two events don't influence each other, you can combine their individual probabilities using two different rules depending on what you're asking. P(A and B) — the chance both happen — is found by multiplying: P(A) × P(B). P(A or B) — the chance at least one happens — is found by adding the two probabilities and subtracting the overlap so it isn't double-counted: P(A) + P(B) − P(A and B).

Worked Example

A weather report gives a 30% chance of rain (event A) and, independently, a 20% chance a flight is delayed for unrelated mechanical reasons (event B).

  1. Step 1: P(A and B) = 0.30 × 0.20 = 0.06, or 6% — the chance both happen
  2. Step 2: P(A or B) = 0.30 + 0.20 − 0.06 = 0.44, or 44% — the chance at least one happens

Frequently Asked Questions

Two events are independent when the outcome of one has no effect on the outcome of the other — like flipping a coin and rolling a die at the same time. This calculator's AND/OR section assumes independence; if one event's result changes the odds of the other (drawing cards without replacement, for example), you'll need a different, conditional-probability approach.
P(A and B) is the chance both events happen together, which is why it's found by multiplying the two probabilities — it's always the smaller number. P(A or B) is the chance at least one of them happens, found by adding the two probabilities and then subtracting the overlap so it isn't counted twice — it's always the larger number.
"1 in 4" means that out of every 4 equally likely outcomes, 1 matches what you're looking for — the same information as a 25% probability, just expressed as a ratio instead of a percentage. Odds phrasing is common in everyday language, while decimals and percentages are more common in formal statistics.
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