STATS Module 4

• Experiment


  A process that, when performed, results in one and only one of many observations. None of the observations can be predicted with certainty.
• Outcomes


  The observations resulting from an experiment
• Sample space


  The collection of all outcomes for an experiment
• Sample points


  The elements of a sample space
• The sample space for an experiment can also be illustrated by drawing a tree diagram
• In a tree diagram, each outcome is represented by a branch of the tree
• Tree diagrams help us understand probability concepts by presenting them visually
• Event


  A collection of one or more of the outcomes of an experiment
• Simple event


  An event that includes one and only one of the (final) outcomes for an experiment
• Compound event


  A collection of more than one outcome for an experiment
• Probability is a numerical measure of the likelihood that a specific event will occur
• Properties of probability


  • The probability of an event always lies in the range 0 to 1
  • The sum of the probabilities of all simple events (or final outcomes) for an experiment, denoted by ΣP(Ei), is always 1

  
• Classical probability


  Two or more outcomes that have the same probability of occurrence are said to be equally likely outcomes

  
• Classical probability rule to find probability

  P(A) = Number of outcomes favorable to A / Total number of outcomes for the experiment

  
• Probability of obtaining a head and a tail in one toss of a coin

  • P(head) = 1/2 = 0.50
  • P(tail) = 1/2 = 0.50

  
• Probability of obtaining an even number in one roll of a die


  • P(even number) = 3/6 = 0.50
• Probability of obtaining a number less than 5 in one roll of a die

  • P(number less than 5) = 4/6 = 0.67
• Probability of obtaining a number greater than 5 in one roll of a die


  • P(number greater than 5) = 1/6 = 0.167
• Relative frequency concept of probability


  Using the frequency of an event's occurrence relative to the total number of trials as an approximation of the probability of that event
• The Law of Large Numbers states that if an experiment is repeated again and again, the probability of an event obtained from the relative frequency approaches the actual (or theoretical) probability

  
• Subjective probability


  The probability assigned to an event based on subjective judgment, experience, information, and belief
• There are no definite rules to assign subjective probabilities
• Marginal probability, conditional probability, and related probability concepts can be used to analyze the data in a two-way classification table

  
• y approaches


  the actual (or theoretical) probability
• THREE CONCEPTUAL APPROACHES TO PROBABILITY

  • Subjective probability
  • Objective probability
  • Relative frequency
• Assume that every employee responds either in favor or against
• Marginal probability


  The probability of a single event without consideration of any other event
• Conditional probability


  The probability that an event will occur given that another has already occurred
• Mutually exclusive events


  Events where the occurrence of one event excludes the occurrence of the other event(s)
• Independent events


  Events where the occurrence of one does not affect the probability of the occurrence of the other
• Complement of an event A

  The event that includes all the outcomes for an experiment that are not in A
• Intersection of events A and B

  The collection of all outcomes that are common to both A and B
• Mutually exclusive events


  Events where the joint probability is always zero
• P(A)


  Probability of event A
• P(A and B)


  Probability of events A and B occurring together
• P(B|A)


  Probability of event B given that event A has occurred
• P(B|A) = P(A and B) / P(A)


  Formula to calculate conditional probability
• P(A and B) = 0 for mutually exclusive events A and B
• Union of events A and B


  Collection of all outcomes that belong to either A or B or to both A and B
• P(A or B) = P(A) + P(B) - P(A and B)


  Addition rule for mutually non-exclusive events