How do you calculate probability?

Q: What types of probability can this calculator compute?

This calculator handles: single event probability, complementary probability, probability of A or B (union), probability of A and B (intersection), conditional probability, and probability of independent/dependent events. It shows formulas and step-by-step solutions.

Q: What is the difference between independent and dependent events?

Independent events don't affect each other: P(A and B) = P(A) × P(B). Example: flipping a coin twice. Dependent events affect each other's probability: P(A and B) = P(A) × P(B|A). Example: drawing cards without replacement. The second draw depends on the first.

Q: What is conditional probability?

Conditional probability is the probability of event A given that event B has already occurred: P(A|B) = P(A and B) / P(B). Example: the probability of drawing an ace from a deck given that the card is a spade is P(Ace|Spade) = 1/13 ≈ 7.7% (only one ace of spades out of 13 spades).

Q: How do I calculate odds from probability?

Odds = Probability / (1 - Probability). For example, if the probability is 0.25 (25%), the odds are 0.25 / 0.75 = 1:3 (read as '1 to 3'). Conversely, to convert odds to probability: P = Odds / (Odds + 1). Odds of 3:1 give P = 3/4 = 75%.

Q: What is the law of large numbers?

The law of large numbers states that as the number of trials increases, the experimental probability approaches the theoretical probability. Flip a coin 10 times and you might get 70% heads. Flip it 10,000 times and it will be very close to 50%. This is why casinos always profit in the long run.

Question

How do you calculate probability?

Accepted Answer

Basic probability = Favorable outcomes / Total outcomes. For independent events: P(A and B) = P(A) × P(B). For mutually exclusive: P(A or B) = P(A) + P(B).

🎲 Probability Calculator