Introductory Statistics

Probability Heads or Tails Parents Getting a Girl Blood Type Getting Brown Eyes Rolling a Seven in a game of monopoly Probability of Getting Rained Upon in a Picnic Winning in Roulette Winning a Million Dollars in the Lottery Rare or Unusual Events (Term to Know in Inferential Statistics)

Three Probability Rules The probability of any event must be greater than or equal to 0 –and- less than or equal to 1. Sum of all Probabilities of all possible outcomes must equal 1. If E represents an event, P(E) is the probability of that event, then the probability of that event not happening is 1-P(E) – Complement Rule.

Three Probability Rules The probability of any event must be greater than or equal to 0 –and- less than or equal to 1. Sum of all Probabilities of all possible outcomes must equal 1. If E represents an event, P(E) is the probability of that event, then the probability of that event not happening is 1-P(E) – Complement Rule. Example Two True Probability Model? Yes – First two rules apply Probability of only getting one head in two flips? 50% Probability of not getting one head in two flips (0 or 2 heads)? 1-50%=50% Example One True Probability Model? No – Second Rule Doesn’t apply

Three Probability Rules –Page 2 Example Three – Empirical Data What is the probability of drawing a brown M&M? What is the probability of not drawing a brown M&M? What is the probability of not drawing a yellow M&M? Example Four – # of girls with three children (assuming the same likelihood for boy/girl) What is the probability of getting exactly two girls? What is the probability of not getting exactly two girls? What is the probability of getting no more than one girl? /8 5/8 4/8 = 1/2

Mean of Discrete Random Variable Mean = (0 * 0.25) + (1 *0.50) + (2 *.25) = = 1 Mean and Variance of Discrete Random Variable