STAT 1000 Lecture Notes - Lecture 7: Conditional Probability
Document Summary
Probability: general addition rule: for any 2 events a and b: the probability that a occurs, b occurs, or both events occur is p(a or b)=p(a) +p (b)-p(a and b). Ex: probability of randomly drawing either an ace or a heart from deck. P (ace or heart)=p (ace) + p (heart) -p (ace and heart) Disjoint events are a special case of the general addition rule. General addition rule: p (a or b)= p(a)+p(b)-p(a and b). Two events are disjoint if they cannot occur at same time. P (a or b) = p(a) + p(b)-0= p(a) +p(b). Conditional probability: reflect how probability of an event can change if we know that some other event has occured/is occuring. Can update degree of belief based on pieces of evidence. Ex: probability that a cloudy day will result in rain different in san diego than in pittsburgh.
