📘 What is Probability?
Probability quantifies the chance that a specific event will occur. It ranges from 0 (impossible) to 1 (certain), often expressed as a fraction, decimal, or percentage.
In simple terms: Probability = (Number of favorable outcomes) / (Total number of possible outcomes).
🧮 How to Use This Calculator
Single Event: Enter the count of favorable outcomes and the total possible outcomes. The tool instantly computes the probability, percentage, and "1 in X" odds.
Two Events: Provide the probabilities of event A and event B (as percentages). Choose the relationship:
- Independent: Occurrence of one does not affect the other (e.g., flipping two coins).
- Mutually Exclusive: Both cannot happen at the same time (e.g., rolling a 2 and a 5 on one die).
- Custom: Manually enter the joint probability P(A and B).
The calculator displays P(A and B), P(A or B), and conditional probabilities P(A|B) and P(B|A) with formulas.
🔢 Key Probability Formulas
Single event: P(E) = favorable / total
Complement: P(not E) = 1 – P(E)
Union (A or B): P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Intersection (A and B):
- Independent: P(A ∩ B) = P(A) × P(B)
- Mutually exclusive: P(A ∩ B) = 0
Conditional Probability: P(A|B) = P(A ∩ B) / P(B), provided P(B) > 0.
💡 Worked Examples
Example 1: Rolling a Die
You want the probability of rolling a number greater than 4 on a fair six‑sided die. Favorable outcomes: {5, 6} → 2. Total outcomes: 6. Probability = 2/6 ≈ 0.3333 (33.33%).
Example 2: Drawing Cards (Independent)
Event A: drawing a heart (13/52 = 25%). Event B: rolling a 6 on a die (1/6 ≈ 16.67%). Since the card and die are independent, P(A and B) = 0.25 × 0.1667 ≈ 4.17%. P(A or B) = 0.25 + 0.1667 – 0.0417 ≈ 37.5%.
Example 3: Mutually Exclusive Events
Picking a red card (50%) and a black card (50%) from a standard deck in one draw – these are mutually exclusive. P(red and black) = 0. P(red or black) = 50% + 50% = 100%.
❓ Frequently Asked Questions
What does "1 in X" mean? It’s the reciprocal of the probability. For example, a probability of 0.25 means "1 in 4".
Can probability be greater than 1 or 100%? No. If your inputs yield a result above 1 (or 100%), it usually indicates overlapping events not properly accounted for – check your relationship settings.
When are events independent? If the outcome of one does not influence the other. Multiplication rule applies: P(A and B) = P(A) × P(B).
Why is conditional probability useful? It updates the chance of an event given new information. For instance, "probability of rain given the sky is cloudy" helps in decision‑making.
