All Tools

Probability Calculator

Enter P(A), P(B), and P(A intersection B) to compute union, complement, and conditional probabilities. The Venn diagram highlights each region and step-by-step formulas show the math.

Input

Results

P(A)
0.300000
P(B)
0.500000
P(A ∩ B)
0.100000
P(A ∪ B)
0.700000
P(A')
0.700000
P(B')
0.500000
P(A|B)
0.200000
P(B|A)
0.333333

Venn Diagram

A0.30B0.500.100

Step-by-Step

1. Addition Rule

P(A∪B)=P(A)+P(B)−P(A∩B)=0.3+0.5−0.1=0.7000P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.3 + 0.5 - 0.1 = 0.7000

2. Complement Rule

P(A′)=1−P(A)=1−0.3=0.7000P(A') = 1 - P(A) = 1 - 0.3 = 0.7000

3. Conditional Probability

P(A∣B)=P(A∩B)P(B)=0.10.5=0.2000P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.1}{0.5} = 0.2000

Reference Guide

Addition Rule

The probability of A or B occurring equals the sum of their individual probabilities minus the overlap.

P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B)

Multiplication Rule

For independent events, the probability of both occurring is the product of each.

P(A∩B)=P(A)×P(B)(if independent)P(A \cap B) = P(A) \times P(B) \quad \text{(if independent)}

Conditional Probability

The probability of A given that B has occurred narrows the sample space to B.

P(A∣B)=P(A∩B)P(B)P(A|B) = \frac{P(A \cap B)}{P(B)}

Complement Rule

The probability of an event not happening equals one minus the probability of it happening.

P(A′)=1−P(A)P(A') = 1 - P(A)