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STA 2023

STA 2023. Basic Concepts of Probability and Counting. Probability Experiments. A probability experiment is an action, or trial, through which specific results are obtained. The result of a single trial is an outcome.

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STA 2023

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  1. STA 2023 Basic Concepts of Probability and Counting

  2. Probability Experiments • A probability experiment is an action, or trial, through which specific results are obtained. • The result of a single trial is an outcome. • The set of all possible outcomes of a probability experiment is the sample space. • An event is a subset of the sample space which may have more than one outcome.

  3. Example 1: Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. • Tossing three Coins. • Sample space: {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} • Number of Outcomes: 8

  4. Simple Event • A simple event is an event that consist of a single outcome. • Example 2: For each event, determine the number of outcomes and state whether the event is simple or not. • Rolling an even number on a six-sided die. • 3 outcomes, not a simple event • Pulling the Queen of Hearts out of a standard deck of playing cards. • 1outcome, simple event.

  5. The Fundamental Counting Principle

  6. Example 3: A shirt company has 4 designs each of which can be made with short or long sleeves. There are 7 color patterns available. How many different shirts are available from this company? • 56 shirts • Example 4: How many license plates can be made consisting of 2 letters followed by 3 digits? • 676,000 license plates

  7. Types of Probability

  8. Example 5: Identify the type of probability being used • The probability that a train will be in an accident on a specific route is 1% • Empirical • The probability that interest rates will rise during the summer is 0.05. • Subjective • The probability of winning California's Pick Three lottery is 1/1000. • Classical

  9. Other Properties • Law of Large Numbers • As an experiment is repeated over and over, the empirical probability of an event approaches the theoretical probability of the event • Range of Probabilities • The probability of an event E is between 0 and 1, inclusive. • Complements • The complement of event E is the set of all outcomes in a sample space that are not included in event E. • Denoted as E’ (e prime)

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