3.2, 3,3 - Conditional Probability (2/4)

Marginal Probability: Based on 1 variable

Joint Probability: Based on 2 variables

Conditional Probability: The probability of an event occurring given that another event has already occurred. This is often expressed as P(A|B), Read as “ The probability of A given (if) B has occurred”

  • Formula: P(A|B) = P(A&B)P(B)\frac{P\left(A\&B\right)}{P\left(B\right)}

For independent events: P(A & B) = P(A) x P(B)

For independent or dependent events: P(A & B) = P(A) P(B|A)

With replacement → Independent events, as the outcome of the first event does not affect the outcome of the second event.

Without replacement → Dependent events, as the outcome of the first event impacts the probability of the second event occurring.

Independence, Conditional Probabilites

If P(A & B) = P(A) P(B), then A and B are independent. A does not affect B

OR

If