Probability

Calculate likelihood of events occurring

Probability Theory

Probability measures the likelihood of an event occurring. It ranges from 0 (impossible) to 1 (certain).

Experiment: A process that produces an outcome

Sample Space: All possible outcomes

Event: One or more specific outcomes

P(Event) = Number of Favorable Outcomes / Total Number of Possible Outcomes

Example: Rolling a die and getting 5

P(5) = 1 / 6 ≈ 0.167 or 16.7%

Independent Events: One event doesn't affect another

P(A and B) = P(A) × P(B)

Dependent Events: One event affects the other

P(A then B) = P(A) × P(B|A)

Mutually Exclusive: Events that can't happen together

P(A or B) = P(A) + P(B)

Permutations: Order matters. P(n,r) = n! / (n-r)!

Combinations: Order doesn't matter. C(n,r) = n! / (r!(n-r)!)