AND Probability Calculator
Compute P(A and B), P(A or B) and conditional probabilities
Enter probabilities or raw counts for two events A and B. This calculator finds the probability of both events happening together (P(A ∩ B)), the union P(A ∪ B), and conditional probabilities like P(A | B) and P(B | A).
If you uncheck independence, you’ll need to provide P(A and B) as well.
You can use either the probability section or the counts section. If both are filled, the calculator will use the probability inputs first.
Results
P(A or B) is calculated as P(A) + P(B) − P(A and B). Conditional probabilities are only shown when the denominators are non-zero.
How this calculator works
- AND probability: P(A ∩ B) = P(A and B).
- For independent events: P(A ∩ B) = P(A) × P(B).
- Union: P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
- Conditionals: P(A | B) = P(A ∩ B) ÷ P(B), P(B | A) = P(A ∩ B) ÷ P(A).
- Counts are converted to probabilities using P = n / N.
How to Calculate AND Probability?
Probability is confusing, especially when the events happen simultaneously. Well, that’s exactly what this calculator solves. Instead of getting lost in formulas like P(A ∩ B) or trying to remember when to multiply or subtract probabilities, this tool automatically breaks everything down for you.
Whether you are a student, teacher, data analyzer, or simply curious about how two events interact, the AND Probability Calculator will give instant, clear results.
Let’s walk through how it works, step by step in totally simple language.
Understanding the Basics — What Does “AND Probability” Mean?
Before using the calculator, it is helpful to know the idea behind it.
When we say P(A and B), we mean:
What’s the probability of event A happening and event B occurring at the same time?
Some examples:
What is the probability that it will rain and the temperature is above 30°?
What’s the probability that a student passed both Math and Science?
What is the probability that a person selects a red card and a number card?
In real life, this is a very common idea, and the calculator helps you compute it instantly.
Two Ways to Use This Calculator
Our calculator gives you two different methods because people have different types of data.
1. Entering Probabilities Directly
This approach is easiest if you already know P(A) and P(B), or you can estimate them.
You enter:
P(A) → probability of event A
P(B) → probability of event B
P(A and B) → optional (only needed if events aren’t independent)
You can select between:
decimals (0–1)
percentages (0–100%)
Hence, this makes things easy for all.
2. Entering Raw Counts (Outcomes)
Sometimes you don’t know the probabilities themselves but you do know the counts.
Example:
Total students = 100
Passed math = 60
Passed Science = 55
Passed both = 40
This calculator automatically converts these numbers into probabilities.
That is very helpful for surveys, experiments, school data, or any real-world data set.
Magic Behind the Calculator: Simple Explanation
Once you enter your values, the calculator computes six main results:
1. P(A)
The probability that A occurs.
If using counts:
P(A) = n(A) / N
2. P(B)
Probability of B occurring.
3. P(A and B)
This is the AND probability.
If events are independent, the calculator uses:
P(A and B) = P(A) × P(B)
If they are not independent, you can manually input P(A and B).
4. P(A or B)
This is the probability that A occurs or B occurs or both.
Formula:
P(A or B) = P(A) + P(B) − P(A and B)
This is one of the most common probability formulas, and often the “subtract” part gets forgotten.
This calculator never forgets.
5. P(A | B) — Conditional Probability
This means:
Probability of A happening given that B already happened.
Formula:
P(A | B) = P(A and B) / P(B)
as long as P(B) > 0.
6. P(B | A)
Similar to above:
P(B | A) = P(A and B) / P(A)
The best part?
None of these formulae need to be committed to memory; your calculator will perform them all for you in a split second.
A Simple Real-Life Example
Suppose you are studying exam results in a class of 100 students.
60 passed Math
55 passed English
35 passed both subjects
Let’s plug these into the calculator.
Step 1 — Enter counts
Total outcomes = 100
n(A): 60
n(B): 55
n(A and B): 35
Step 2 – Click “Calculate”
Here’s what the calculator will say:
P(A) = 0.60 (60%)
That means 60% of students passed Math.
P(B) = 0.55 (55%)
55% of the students passed English.
P(A and B) = 0.35 (35%)
35% of students passed both subjects.
P(A or B) = 0.80 (80%)
The formula is:
60% + 55% – 35% = 80%
So, 80% of the students passed at least one of the two subjects.
P(A | B) ≈ 0.636 (63.6%)
Meaning:
Given that a student has passed in English, the probability that he/she also passed in Math is about 63.6%.
P(B | A) ≈ 0.583 (58.3%)
Meaning:
The probability of passing English, given that a student has passed Math, is approximately 58.3%.
Everything is transparent, structured, and represented both in decimal and percent form.
Why This Calculator Is So Useful
People love this calculator because it:
✔ It removes the stress of formulas
Even if you haven’t studied statistics in years, you can still understand your results.
✔ It works for both probability and real-life data
You can use percentages, decimals, or raw counts.
✔ It auto-detects independent events
and calculates AND probability for you.
Ideal for both students and teachers.
Homework or assignments, or studying for exams, becomes much easier.
It’s super mobile-friendly
You can easily calculate complex probabilities using your phone.
In a Nutshell
Turn confusing math into something anyone can conceptualize with this AND Probability Calculator.
You tell it:
What is the probability of A?
What is the probability of B?
Are they independent?
How many outcomes did you observe? …and it instantly tells you: P(A) P(B) P(A and B) P(A or B) P(A | B) P(B | A) clean, fast, accurate, human-friendly.