STATISTIC :PROBABILITY Experiment Any operation or procedure whose outcome cannot be predicted with certainty. Outcomes for an experiment is called sample space. Example 1.The single toss of a coin is an experiment whose outcome cannot be predicted with certainty. The sample space consist of two outcomes, heads or tails. The letter S could be used to represent the Sample Space and maybe represented as S={H,T}. 2. When a quality control technician selects and item from a production line, it maybe classified as defective or non-defective. The sample space may be represented by S={D,N}

STATISTIC :PROBABILITY Event, Simple events and Compound Events Event is a subset of the sample space consisting at least one outcome from the sample space. If the event consist of exactly one outcome, it is called a simple event If an event consists of more than one outcome, it is called a compound event Example 1 A quality control technician selects two computer and classifies each as defective or non-defective. The sample space maybe represented as S = {NN,ND,DN,DD}, where D represents a defective unit and N represents a non-defective unit. Let A represent the event that neither unit is defective and let B represent at least one of the units is defective. A = {NN} is a simple event and B={ND,DN,DD} is a compound event

STATISTIC :PROBABILITY Event, Simple events and Compound Events Example 2 An experiment is conducted whereby five people is examine to determine their blood types. The compound event where all five has the same blood type is composed of the following four outcomes : (A,A,A,A,A) (B,B,B,B,B) (AB,AB,AB,AB) and (O,O,O,O,O). The simple event that all five have blood type O would be the outcome (O,O,O,O,O).

STATISTIC :PROBABILITY PROBABILITY Measure the likelihood of the occurrence of some event. The probability of any event E is represented by the symbol P(E) and the symbol read a “P of E” or “the probability of event E” P(E) is a real number between zero and 1 = 0 ≤ P(E) ≤ 1 The sum of probabilities for all simple events of an experiment must equal to 1 P(E 1 ) + P(E 2 )+…P(E n ) = 1 or P(S) = 1 The classical definition of probability is appropriate when all outcomes of an experiment are equally likely. For experiment with n outcomes, classical definition of probability assigns probability to each outcome or simple event. For event E consisting k outcomes, the probability of event E is given by 1n1n knkn P(E) =

Waiting Time For Transplant Type of TransplantLess than one yearOne year or More Heart105 Kidney73 Liver55 Pancreas32 Eyes55 Table 4.0 = 15 = 20

STATISTIC :PROBABILITY PROBABILITY continue… Example Table 4.0 gives information concerning 50 organ transplants in the state of Selangor during a recent year. Each patient had only one transplant ( = ). If one of 50 patient record randomly selected, the probability that the patient had a heart Transplant is = 0.30 ( ) since 15 patients had a heart transplant. The Probability that the patient had to wait one year or more is for a transplant is = 0.40 since 20 of the patients had to wait a year or more. 1n1n knkn 20 50

Exercise Q1 An experiment consist of using a 25- question test instrument to classify an individual as having either type A or type B personality. Supposed 3 individuals are classified as to personality type. Give the sample space for this experiment. Give one simple event example and one compound event example. Q2 In an actuarial study,9,875 females out of 10,000 females who are age 20 live to be 30 years old. What is the probability that a 20 year old female will live to be 30 years old. S = { } A = { } simple event B={ } compound event knkn P(E) =