Probability of Events

Analyze how two events interact. Calculate unions, intersections, and conditional odds.

Probability of A - P(A)

Probability of B - P(B)

Mutually Exclusive Independent

Intersection - P(A ∩ B)

                    0.70
                    Union P(A ∪ B)
                

0.50 P(A | B)

0.40 P(B | A)

0.50 Comp. P(A')

0.60 Comp. P(B')

Probability Rules

Understanding the relationship between events is key to accurate statistical modeling.

Union (OR): The probability that at least one of the events occurs. For any two events, P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Intersection (AND): The probability that both occur at the same time.
Independent Events: Events are independent if the occurrence of one does not affect the other. In this case, P(A ∩ B) = P(A) × P(B).
Mutually Exclusive: Events that cannot happen at the same time (like rolling a 1 and a 2 on a single die). For these, P(A ∩ B) = 0.
Conditional Probability: The probability of A happening given that B has happened: P(A | B) = P(A ∩ B) / P(B).