Statistics for Decision Making Ch. 4

Collectively Exhaustive

A set of events are collectively exhaustive if when at least one of the events has to occur, i.e. all possible events are included in this set.

Multiplication Rule for any Two Events

P(E1 and E2)= P(E1)P(E2|E1)

Addition Rule for any Two Events

P(E1 or E2)= P(E1) + P(E2) - P(E1 and E2)

Conditional Probability for any Two Events

The conditional probability that E1 will occur given that E2 has already occurred is given by: Where P(E2)>0

Independent Events

Two events are independent if the occurrence of one event in no way influences the probability of the occurrence of the other event.

Mutually Exclusive Events

Two events are mutually exclusive if the occurrence of one event precludes the occurrence of the other event.