Page 1 of 2 Introduction to Probability for Statistics 0401-Probability.doc Introduction to Probability for Statistics Recall that we are studying two types of statistics – descriptive statistics and inferential statistics. In order for us to move to inferential statistics, we need a certain level of understanding of probability. In this section, we will study the basics of probability needed to study inferential statistics later. This section covers the basics of probability in three subsections: fundamentals, addition rule, and multiplication rule – basic. Fundamentals Event – collection of results or outcomes of procedure. Simple event – event or outcome that cannot be broken down (simplified) any more. Sample space – all possible simple events or outcomes. Rule 1: Relative Frequency Approach (based on past experience) P( A) number of occurances of A number of successes total number of trials total number of trials Rule 2: Classical Approach (equally likely outcomes) P( A) number of ways Acan occur s total number of sample events n Rule 3: Subjective Approach – estimating or guessing P(A) based on knowledge of circumstances. Unusual event – If P(A) 0.05, then event A is said to be an unusual event. Law of Large Numbers – as the number of trials increase, the relative frequency probability approaches the actual probability. Complement of event A is A equals all outcomes not containing event A. Rounding answers: exact fraction or decimal of three significant digits. 0 P(A) 1. P( A) a (in reduced form). a : b or a to b. P( A) b P ( A) b (in reduced form) b : a or b to a. Odds in favor of event A = P ( A) a net profit Pay off odds against event A = amount bet Odds against event A = Introduction to Probability for Statistics 0401-Probability.doc Page 2 of 2 Addition Rule Compound event – two or more simple events. Addition rule: P(A or B) = P(A) + P(B) – P(A and B) Mutually exclusive events A and B cannot occur simultaneously. If A and B are mutually exclusive, then A and B have nothing in common and P(A or B) = P(A) + P(B) because P(A and B) = 0. Rule of Complementary Events: If A and A are complementary events, then P(A) + P( A ) = 1 or P(A) = 1 – P( A ) or P A ) = 1 – P(A) Multiplication Rule - Basic P(A and B) = P(event A occurs and event B occurs) Conditional Probability: P(B|A) = P(event B occurs after event A has already occurred) Independent events: occurrence of one does not affect the probability of the occurrence of the other event. P(A and B) = P(A)P(B|A) general rule If A and B are independent, P(A and B) = P(A)P(B) because P(B|A) = P(B). Common guideline for use of independent vs. dependent: If a sample size is 5% of population size, treat the selections as being independent (even if selections are without replacement; they are technically dependent).