Comprehensive Calculator Guide
This calculator finds P(A|B), the chance of A once B is known, plus P(B|A), and tests independence. If 40% study maths, 50% physics and 15% both, a physics student studies maths with probability 0.15 ÷ 0.5 = 0.3.
Conditioning
Divide the joint probability by the probability of what you know. P(A|B) and P(B|A) usually differ; Bayes’ theorem turns one into the other. Events are independent when P(A and B) = P(A) × P(B).
How to Use
- Enter P(A) and P(B).
- Enter P(A and B).
- Press “Calculate” to see P(A|B), P(B|A) and independence.
Formula Used
P(A|B) = P(A and B) ÷ P(B) | P(B|A) = P(A and B) ÷ P(A)
Practical Examples
- Example 1
- 0.4, 0.5, 0.15: P(A|B) = 0.3, P(B|A) = 0.375, dependent.
- Example 2
- 0.3, 0.5, 0.15: independent.
Important Tips
- Draw a table or Venn diagram.
- The known event goes after the bar.
- Compare P(A|B) with P(A).
Common Mistakes to Avoid
- Swapping the direction.
- Dividing by the wrong probability.
- A joint probability above either single one.
Frequently Asked Questions
- What does P(A|B) mean?
- The chance of A given B.
- How do I test independence?
- Check P(A and B) = P(A) × P(B).
- Link to Bayes?
- Bayes flips the direction.