Enter favourable and total outcomes for a single event, or combine two events as mutually exclusive or independent.
Probability Calculator
Combined Events
How It’s Calculated
The basic definition: P(A) = favourable outcomes ÷ total outcomes. For two events, mutually exclusive means A and B can never happen together (like rolling a 2 and a 5 on one die), so P(A∪B) = P(A) + P(B). Independent means one event doesn’t affect the other’s probability (like two separate coin tosses), so P(A∩B) = P(A) × P(B), and the general addition rule P(A∪B) = P(A) + P(B) − P(A∩B) still applies.
Worked Example
Rolling a fair die: P(getting a 4) = 1/6. For two independent coin tosses, P(heads on both) = 0.5 × 0.5 = 0.25.
Frequently Asked Questions
Q: What’s the difference between mutually exclusive and independent?
Mutually exclusive events can’t both occur in a single trial (P(A∩B)=0). Independent events can both occur, and one doesn’t influence the other’s chance — they’re different relationships and mixing them up is a common exam error.
Q: Can probability be greater than 1?
Never — it’s always between 0 and 1. If a calculation gives you more than 1, double-check the favourable and total outcome counts.
Distinguishing mutually exclusive from independent events is one of the most tested ideas in 1st PUC Probability. See how Daniel Classes teaches 1st and 2nd PUC Mathematics →