5.3 Independence and The Multiplication Rule (unit 2)

Rules of Probability (#3-5)

3. If E and F are disjoint events then, P(E or F) = P(E) + P(F) If E and F aren't disjoint then, P(E or F)= P(E)+P(F)-P(E & F) 4. if E represents any event and E^c represents the complement of E, then P(E^c)= 1 - P(E) 5. if E and F are independent events, then P(E and F)= P(E)xP(F)

Compute At-Least Probability Using Complement Rule

P(at least one is X) = 1 - P(none is X) P(at least one is not X) = 1 - P(all are X)

AND event

a outcome is in the event A and B if the outcome is in both A and B at the same time ex. A= {1, 2, 3, 4, 5} and B= {4, 5, 6, 7, 8}. then A and B= {4,5}

Multiplication Rule for Independent events (AND events)

if E anf F are independent events, then P(E an F) = P(E) x P(F)

Multiplication rule for n Independent Events

if E1, E2, E3,... and En are independent events then, P(E1 and E2 and E3 and .... En) = P(E1) x P(E2) x P(E3) ... x P(En)

independent events

two events E and F are independent if the occurence of event E in a probability experiement does not affect the probability of event F

dependent events

two events are dependent if the occurance of event E in a probability experiement affects the probability of event F.