Comprehensive Calculator Guide
This calculator takes the probabilities of two independent events and gives the chance of both, at least one, exactly one and neither. With 0.8 and 0.7, both happen with probability 0.56 and at least one with 0.94.
The rules
For independent events multiply: P(A and B) = 0.8 × 0.7 = 0.56. For “A or B” add and subtract the overlap: 0.8 + 0.7 − 0.56 = 0.94. Or use the complement: 1 − 0.2 × 0.3 = 0.94.
How to Use
- Enter P(A) between 0 and 1.
- Enter P(B).
- Press “Calculate” to see both, at least one, exactly one and neither.
Formula Used
P(A and B) = P(A) × P(B) | P(A or B) = P(A) + P(B) − P(A and B)
Practical Examples
- Example 1
- 0.8 and 0.7: both 0.56, at least one 0.94, exactly one 0.38.
- Example 2
- A coin and a number cube showing 6: both about 0.0833.
Important Tips
- Check independence first.
- Convert percentages to decimals.
- Use the complement for “at least one”.
Common Mistakes to Avoid
- Adding without subtracting the overlap.
- Multiplying dependent events.
- Mixing up “at least one” and “exactly one”.
Frequently Asked Questions
- What are independent events?
- One happening doesn’t change the other’s chance.
- Independent vs mutually exclusive?
- Mutually exclusive events can’t happen together.
- Dependent events?
- Use P(A) × P(B|A).